System and method for estimating a treatment volume for administering electrical-energy based therapies

ABSTRACT

The invention provides for a system for estimating a 3-dimensional treatment volume for a device that applies treatment energy through a plurality of electrodes defining a treatment area, the system comprising a memory, a display device, a processor coupled to the memory and the display device, and a treatment planning module stored in the memory and executable by the processor. In one embodiment, the treatment planning module is adapted to generate an estimated first 3-dimensional treatment volume for display in the display device based on the ratio of a maximum conductivity of the treatment area to a baseline conductivity of the treatment area. The invention also provides for a method for estimating 3-dimensional treatment volume, the steps of which are executable through the processor. In embodiments, the system and method are based on a numerical model which may be implemented in computer readable code which is executable through a processor.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation of U.S. patent applicationSer. No. 15/011,752 filed Feb. 1, 2016 (which published as U.S. PatentApplication Publication No. 2016/0143698 on May 26, 2016 and whichissued as U.S. Pat. No. 10,470,822 on Nov. 12, 2019). The '752application is a Continuation of U.S. patent application Ser. No.14/012,832 filed Aug. 28, 2013 (which published as U.S. PatentApplication Publication No. 2013/0345697 on Dec. 26, 2013 and issued asU.S. Pat. No. 9,283,051 on Mar. 15, 2016 and which relies on and claimsthe benefit of the filing date of U.S. Provisional Application No.61/694,144, filed on Aug. 28, 2012), which '832 application is aContinuation-in-Part (CIP) application of U.S. application Ser. No.12/491,151, filed Jun. 24, 2009 (which issued as U.S. Pat. No. 8,992,517on Mar. 31, 2015 and which claims priority to and the benefit of thefiling dates of U.S. Provisional Patent Application Nos. 61/171,564,filed Apr. 22, 2009, 61/167,997, filed Apr. 9, 2009, and 61/075,216,filed Jun. 24, 2008), and which '151 application is a CIP application ofU.S. patent application Ser. No. 12/432,295, filed Apr. 29, 2009 (whichpublished as U.S. Patent Application Publication No. 2009/0269317 onOct. 29, 2009 and issued as U.S. Pat. No. 9,598,691 on Mar. 21, 2017 andwhich claims priority to and the benefit of the filing date of U.S.Provisional Patent Application No. 61/125,840, filed Apr. 29, 2008). Thedisclosures of these patent applications are hereby incorporated byreference herein in their entireties.

FIELD OF THE INVENTION

The present invention is related to medical therapies involving theadministering of electrical treatment energy. More particularly,embodiments of the present invention provide systems and methods forestimating a target ablation zone for a medical treatment device thatapplies electrical treatment energy through a plurality of electrodesdefining a target treatment area.

DESCRIPTION OF RELATED ART

Electroporation-based therapies (EBTs) are clinical procedures thatutilize pulsed electric fields to induce nanoscale defects in cellmembranes. Typically, pulses are applied through minimally invasiveneedle electrodes inserted directly into the target tissue, and thepulse parameters are tuned to create either reversible or irreversibledefects. Reversible electroporation facilitates the transport ofmolecules into cells without directly compromising cell viability. Thishas shown great promise for treating cancer when used in combinationwith chemotherapeutic agents or plasmid DNA (M. Marty et al.,“Electrochemotherapy—An easy, highly effective and safe treatment ofcutaneous and subcutaneous metastases: Results of ESOPE (EuropeanStandard Operating Procedures of Electrochemotherapy) study,” EuropeanJournal of Cancer Supplements, 4, 3-13, 2006; A. I. Daud et al., “PhaseI Trial of Interleukin-12 Plasmid Electroporation in Patients WithMetastatic Melanoma,” Journal of Clinical Oncology, 26, 5896-5903, Dec.20, 2008). Alternatively, irreversible electroporation (IRE) has beenrecognized as non-thermal tissue ablation modality that produces atissue lesion, which is visible in real-time on multiple imagingplatforms (R. V. Davalos, L. M. Mir, and B. Rubinsky, “Tissue ablationwith irreversible electroporation,” Ann Biomed Eng, 33, 223-31, February2005; R. V. Davalos, D. M. Otten, L. M. Mir, and B. Rubinsky,“Electrical impedance tomography for imaging tissue electroporation,”IEEE Transactions on Biomedical Engineering, 51, 761-767, 2004; L.Appelbaum, E. Ben-David, J. Sosna, Y. Nissenbaum, and S. N. Goldberg,“US Findings after Irreversible Electroporation Ablation:Radiologic-Pathologic Correlation,” Radiology, 262, 117-125, Jan. 1,2012). Because the mechanism of cell death does not rely on thermalprocesses, IRE spares major nerve and blood vessel architecture and isnot subject to local heat sink effects (B. Al-Sakere, F. Andre, C.Bernat, E. Connault, P. Opolon, R. V. Davalos, B. Rubinsky, and L. M.Mir, “Tumor ablation with irreversible electroporation,” PLoS ONE, 2,e1135, 2007). These unique benefits have translated to the successfultreatment of several surgically “inoperable” tumors (K. R. Thomson etal., “Investigation of the safety of irreversible electroporation inhumans,” J Vasc Intery Radiol, 22, 611-21, May 2011; R. E. Neal II etal., “A Case Report on the Successful Treatment of a Large Soft-TissueSarcoma with Irreversible Electroporation,” Journal of ClinicalOncology, 29, 1-6, 2011; P. A. Garcia et al., “Non-thermal irreversibleelectroporation (N-TIRE) and adjuvant fractionated radiotherapeuticmultimodal therapy for intracranial malignant glioma in a caninepatient,” Technol Cancer Res Treat, 10, 73-83, 2011).

In EBTs, the electric field distribution is the primary factor fordictating defect formation and the resulting volume of treated tissue(J. F. Edd and R. V. Davalos, “Mathematical modeling of irreversibleelectroporation for treatment planning,” Technology in Cancer Researchand Treatment, 6, 275-286, 2007 (“Edd and Davalos, 2007”); D. Miklavcic,D. Semrov, H. Mekid, and L. M. Mir, “A validated model of in vivoelectric field distribution in tissues for electrochemotherapy and forDNA electrotransfer for gene therapy,” Biochimica et Biophysica Acta,1523, 73-83, 2000). The electric field is influenced by both thegeometry and positioning of the electrodes as well as the dielectrictissue properties. Because the pulse duration (˜100 μs) is much longerthan the pulse rise/fall time (˜100 ns), static solutions of theLaplace's equation incorporating only electric conductivity aresufficient for predicting the electric field distribution. In tissueswith uniform conductivity, solutions can be obtained analytically forvarious needle electrode configurations if the exposure length is muchlarger than the separation distance (S. Corovic, M. Pavlin, and D.Miklavcic, “Analytical and numerical quantification and comparison ofthe local electric field in the tissue for different electrodeconfigurations,” Biomed Eng Online, 6, 2007; R. Neal II et al.,“Experimental Characterization and Numerical Modeling of TissueElectrical Conductivity during Pulsed Electric Fields for IrreversibleElectroporation Treatment Planning,” Biomedical Engineering, IEEETransactions on, PP, 1-1, 2012 (“Neal et al., 2012”)). This is not oftenthe case in clinical applications where aberrant masses with a diameteron the order of 1 cm are treated with an electrode exposure length ofsimilar dimensions. Additionally, altered membrane permeability due toelectroporation influences the tissue conductivity in a non-linearmanner. Therefore numerical techniques may be used to account for anyelectrode configuration and incorporate a tissue-specific functionrelating the electrical conductivity to the electric field distribution(i.e. extent of electroporation).

Conventional devices for delivering therapeutic energy such aselectrical pulses to tissue include a handle and one or more electrodescoupled to the handle. Each electrode is connected to an electricalpower source. The power source allows the electrodes to deliver thetherapeutic energy to a targeted tissue, thereby causing ablation of thetissue.

Once a target treatment area is located within a patient, the electrodesof the device are placed in such a way as to create a treatment zonethat surrounds the treatment target area. In some cases, each electrodeis placed by hand into a patient to create a treatment zone thatsurrounds a lesion. The medical professional who is placing theelectrodes typically watches an imaging monitor while placing theelectrodes to approximate the most efficient and accurate placement.

However, if the electrodes are placed by hand in this fashion, it isvery difficult to predict whether the locations selected will ablate theentire treatment target area because the treatment region defined by theelectrodes vary greatly depending on such parameters as the electricfield density, the voltage level of the pulses being applied, size ofthe electrode and the type of tissue being treated. Further, it is oftendifficult or sometimes not possible to place the electrodes in thecorrect location of the tissue to be ablated because the placementinvolves human error and avoidance of obstructions such as nerves, bloodvessels and the like.

Conventionally, to assist the medical professional in visualizing atreatment region defined by the electrodes, an estimated treatmentregion is generated using a numerical model analysis such as complexfinite element analysis. One problem with such a method is that even amodest two dimensional treatment region may take at least 30 minutes toseveral hours to complete even in a relatively fast personal computer.This means that it would be virtually impossible to try to obtain on areal time basis different treatment regions based on different electrodepositions.

Therefore, it would be desirable to provide an improved system andmethod to predict a treatment region in order to determine safe andeffective pulse protocols for administering electrical energy basedtherapies, such IRE.

SUMMARY OF THE INVENTION

The inventors of the present invention have made the surprisingdiscovery that by monitoring current delivery through the electrodesplaced for treatment, it is possible to determine the extent ofelectroporation in the tissue and accurately predict the treatmentvolume. In addition to current measurements, the prediction can alsorely on prior knowledge of the tissue-specific conductivity function andelectric field threshold for either reversible electroporation or celldeath in the case of IRE.

The inventors have characterized this non-linear conductivity behaviorin ex vivo porcine kidney tissue. (“Neal et al., 2012”). Using thisinformation, the inventors performed a comprehensive parametric study onelectrode exposure length, electrode spacing, voltage-to-distance ratio,and ratio between the baseline conductivity pre-IRE and maximumconductivity post-IRE. Current measurements from all 1440 possibleparameter combinations were fitted to a statistical (numerical) modelaccounting for interaction between the pulse parameters and electrodeconfiguration combinations. The resulting equation is capable ofrelating pre- and post-treatment current measurements to changes in theelectric field distribution for any desired treatment protocol, such asfor IRE.

The present invention provides a system for estimating a 3-dimensionaltreatment volume based on the numerical models developed. Variousembodiments of this system are summarized below to provide anillustration of the invention.

In one embodiment, the invention provides a system for estimating a3-dimensional treatment volume for a medical treatment device thatapplies treatment energy through a plurality of electrodes defining atreatment area. The system comprises a memory, a display device, aprocessor coupled to the memory and the display device, and a treatmentplanning module stored in the memory and executable by the processor. Inembodiments, the treatment planning module is adapted to generate anestimated first 3-dimensional treatment volume for display in thedisplay device based on the ratio of a maximum conductivity of thetreatment area to a baseline conductivity of the treatment area.

In embodiments of the invention, the treatment planning module can beconfigured such that it is capable of deriving the baseline conductivityand maximum conductivity of the treatment area based on a relationshipof current as a function of W, X, Y and Z, in which:

W=voltage to distance ratio;

X=edge to edge distance between electrodes;

Y=exposure length of electrode.

Z=maximum conductivity/baseline conductivity.

In embodiments, the treatment planning module is operably configuredsuch that it is capable of deriving baseline conductivity using apre-treatment pulse.

In embodiments of the invention, the treatment planning module generatesthe estimated first 3-dimensional treatment volume using a numericalmodel analysis.

In embodiments of the invention, the numerical model analysis includesone or more of finite element analysis (FEA), Modified AnalyticalSolutions to the Laplace Equation, and other Analytical Equations (e.g.,Ellipsoid, Cassini curve) that fit the shape of a specific ElectricField isocontour from the FEA models either by a look-up table orinterpolating analytical approximations.

In embodiments of the invention, the treatment planning module generatesthe estimated first 3-dimensional treatment volume using a set of second3-dimensional ablation volumes according to different W, X, Y and Zvalues, which have been predetermined by a numerical model analysis.

The treatment planning module can generate the estimated first3-dimensional treatment volume using a set of second 3-dimensionalablation volumes according to different W, X, Y and Z values, which havebeen pre-determined by a numerical model analysis; and generating a setof interpolated third 3-dimensional volumes based on the predeterminedset of second 3-dimensional ablation volumes.

In embodiments of the invention, the treatment planning module derivesby curve fitting of one or more of: a mathematical function of x valuesof the ablation volume as a function of any one or more of W, X, Yand/or Z; a mathematical function of y values of the ablation volume asa function of any one or more of W, X, Y and/or Z; and a mathematicalfunction of z values of the ablation volume as a function of any one ormore of W, X, Y and/or Z.

In embodiments, the treatment planning module generates the estimatedfirst 3-dimensional treatment volume using the three mathematicalfunctions.

In embodiments of the invention, the treatment planning module iscapable of measuring a baseline and maximum conductivity of thetreatment area pre-treatment; capable of generating a fourth3-dimensional treatment volume based on the measured baseline andmaximum conductivity; and capable of displaying both the first andfourth 3-dimensional treatment volumes in the display device.

In embodiments, the treatment planning module superimposes one of thefirst and fourth 3-dimensional treatment volumes over the other toenable a physician to compare an estimated result to an actual estimatedresult.

Embodiments of the invention include a method for estimating a3-dimensional treatment volume for a medical treatment device thatapplies treatment energy through a plurality of electrodes define atreatment area, wherein the steps of the method are executable through aprocessor, the method comprising: a) Determining the baseline electricconductivity; b) Determining the maximum electric conductivity; and c)Generating an estimated first 3-dimensional treatment volume based onthe ratio of the maximum conductivity of the treatment area to thebaseline conductivity of the treatment area.

Included within the scope of the invention is a method for estimating atarget ablation zone for a medical treatment device that applieselectrical treatment energy through a plurality of electrodes defining atarget treatment area, the method comprising: determining a baselineelectrical flow characteristic (EFC) in response to delivery of a testsignal to tissue of a subject to be treated; determining, based on thebaseline EFS, a second EFC representing an expected EFC during deliveryof the electrical treatment energy to the target treatment area; andestimating the target ablation zone for display in the display devicebased on the second EFC. Such methods can include where the step ofdetermining a baseline EFC includes determining an electricalconductivity.

In embodiments of the invention, the baseline electric conductivity canbe determined by: i) Initiating a low voltage pre-IRE pulse through aprobe; ii) Measuring the current of the low voltage pre-IRE pulsethrough the probe; iii) Optionally, scaling the current measured in stepii. to match a voltage-to-distance ratio value; and iv) Solving forfactor in the following equation provided in Example 1 to determine thebaseline electric conductivityI=factor·[aW+bX+cY+dZ+e(W−W )(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]

In embodiments of the invention, at least one high voltage IRE pulse isinitiated through the probe, such as after step b, to provide an IREtreatment.

In embodiments of the invention, the maximum electric conductivity isdetermined after the IRE treatment by: i) Providing a low voltagepost-IRE pulse through the probe; ii) Measuring the current of the lowvoltage post-IRE pulse through the probe; iii) Optionally, scaling thecurrent measured in step ii. to match a voltage-to-distance value; andiv) Solving for factor in the following equation provided in Example 1to determine the maximum electric conductivity post-IREI=factor·[aW+bX+cY+dZ+e(W−W )(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]

In another embodiment, the invention provides a system for estimating atarget ablation zone for a medical treatment device that applieselectrical treatment energy through a plurality of electrodes defining atarget treatment area, the system comprising a memory, a display device,a processor coupled to the memory and the display device; and atreatment planning module stored in the memory and executable by theprocessor, the treatment planning module adapted to receive a baselineelectrical flow characteristic (EFC) in response to delivery of a testsignal to tissue of a subject to be treated, determine a second EFCrepresenting an expected EFC during delivery of the electrical treatmentenergy to the target treatment area, and estimating the target ablationzone for display in the display device based on the second EFC.

In embodiments of the invention, the EFC includes an electricalconductivity.

In embodiments of the invention, the second EFC includes a maximumconductivity expected during the delivery of the electrical treatmentenergy to the target treatment area; and the treatment planning moduleestimates the target ablation zone based on the ratio of the second EFCto the baseline EFC.

In embodiments, the treatment planning module estimates the second EFCto be a multiple of the baseline EFC which is greater than 1 and lessthan 6.

The treatment planning module is capable of estimating the second EFC tobe a multiple of the baseline EFC which is greater than 3 and less than4.

Additionally or alternatively, the treatment planning module deliversthe test signal that includes a high frequency AC signal in the range of1 Hz to 100 MHz, such as between 500 kHz and 10 MHz.

In embodiments of the invention, the treatment planning module deliversthe test signal that includes an excitation AC voltage signal of 1 mV to10 mV. The test voltage that can be applied can be in the range of fromabout 1 mV to about 125 V, such as from 1 V to 5 V, or from 3 V to 50 V,such as from 10 V to 100 V, or 50-125 V.

The treatment planning module in embodiments delivers the test signalthat includes a low voltage non-electroporating pre-IRE pulse of 10 V/cmto 100 V/cm.

The treatment planning module in embodiments delivers the test signalthat includes a low voltage non-electroporating pre-IRE pulse of 25 V/cmto 75 V/cm.

In embodiments of the invention, the treatment planning module deliversthe test signal that includes the high frequency AC signal and a DCpulse.

In embodiments of the invention, the treatment planning moduledetermines a third EFC that represents an actual EFC during delivery ofthe electrical treatment energy for confirmation of the estimated targetablation zone.

In embodiments of the invention, the treatment planning moduledetermines the second EFC based on W, X and Y, in which:

W=voltage to distance ratio;

X=edge to edge distance between electrodes;

Y=exposure length of electrode.

In embodiments of the invention the treatment planning module estimatesthe target ablation zone based on a set of predetermined ablation zonesaccording to different W, X, Y and Z values.

The treatment planning module can estimate the target ablation zone bycurve fitting: a mathematical function of x values of the ablationvolume as a function of any one or more of W, X, Y and/or Z; amathematical function of y values of the ablation volume as a functionof any one or more of W, X, Y and/or Z; and/or a mathematical functionof z values of the ablation volume as a function of any one or more ofW, X, Y and/or Z.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate certain aspects of embodiments ofthe present invention, and should not be used to limit or define theinvention. Together with the written description the drawings serve toexplain certain principles of the invention.

Further, the application file contains at least one drawing executed incolor. Copies of the patent application publication with colordrawing(s) will be provided by the Office upon request and payment ofthe necessary fee.

FIG. 1 is a schematic diagram of a representative system of theinvention.

FIG. 2 is a schematic diagram of a representative treatment controlcomputer of the invention.

FIG. 3 is schematic diagram illustrating details of the generator shownin the system of FIG. 1 , including elements for detecting anover-current condition.

FIG. 4 is a flow chart illustrating a method, e.g., algorithm, of theinvention.

FIG. 5 is a graph of the asymmetrical Gompertz function showing tissueelectric conductivity as a function of electric field.

FIG. 6 is a graph showing a representative 3D plot of current [A] as afunction of Z (σ_(max)/σ_(o)) and voltage-to-distance ratio (W) for aseparation distance of 1.5 cm and an electrode exposure length of 2.0 cmas used by Ben-David et al.

FIGS. 7A and 7B are graphs showing representative contour plots ofcurrent [A] as a function of electrode exposure and separation distanceusing 1500 V/cm for Z=1 (FIG. 7A) and Z=4 (FIG. 7B).

FIGS. 8A and 8B are tables showing Whole Model Parameter Estimates andEffect Tests, respectively.

FIG. 8C is a graph showing a plot of Actual Current vs. PredictedCurrent.

FIGS. 9A-9F are graphs showing the representative (15 mm gap)correlation between current vs. exposure length and electrode radius formaximum conductivities (1×-6×, respectively).

FIG. 10A is a table showing experimental validation of the code fordetermining the tissue/potato dynamic from in vitro measurements,referred to as potato experiment #1.

FIG. 10B is a table showing experimental validation of the code fordetermining the tissue/potato dynamic from in vitro measurements,referred to as potato experiment #2.

FIGS. 11A and 11B are graphs plotting residual current versus data pointfor analytical shape factor (FIG. 11A) and statistical (numerical)non-linear conductivity (FIG. 11B).

FIGS. 12A-12C are graphs showing representative contour plots of theelectric field strength at 1.0 cm from the origin using an edge-to-edgevoltage-to-distance ratio of 1500 V/cm assuming z=1, wherein FIG. 12A isa plot of the x-direction, FIG. 12B is a plot of the y-direction, andFIG. 12C is a plot of the z-direction.

FIGS. 13A-13C are 3D plots representing zones of ablation for a 1500V/cm ratio, electrode exposure of 2 cm, and electrode separation of 1.5cm, at respectively a 1000 V/cm IRE threshold (FIG. 13A), 750 V/cm IREthreshold (FIG. 13B), and 500 V/cm IRE threshold (FIG. 13C) using theequation for an ellipsoid.

FIG. 14A is a schematic diagram showing an experimental setup of anembodiment of the invention.

FIG. 14B is a schematic diagram showing dimension labeling conventions.

FIG. 14C is a waveform showing 50 V pre-pulse electrical current at 1 cmseparation, grid=0.25 A, where the lack of rise in intrapulseconductivity suggests no significant membrane electroporation duringpre-pulse delivery.

FIG. 14D is a waveform showing electrical current for pulses 40-50 of1750 V at 1 cm separation, grid=5 A, where progressive intrapulsecurrent rise suggests continued conductivity increase andelectroporation.

FIGS. 15A and 15B are electric field [V/cm] isocontours fornon-electroporated tissue (FIG. 15A) and electroporated tissue (FIG.15B) maps assuming a maximum conductivity to baseline conductivity ratioof 7.0×.

FIGS. 16A and 16B are representative Cassini Oval shapes when varyingthe ‘a=0.5 (red), 0.6 (orange), 0.7 (green), 0.8 (blue), 0.9 (purple),1.0 (black)’ or ‘b=1.0 (red), 1.05 (orange), 1.1 (green), 1.15 (blue),1.2 (purple), 1.25 (black)’ parameters individually. Note: If a>1.0 orb<1.0 the lemniscate of Bernoulli (the point where the two ellipsesfirst connect (a=b=1) forming “∞”) disconnects forming non-contiguousshapes.

FIG. 17 is a graph showing NonlinearModelFit results for the ‘a’ and ‘b’parameters used to generate the Cassini curves that represent theexperimental IRE zones of ablation in porcine liver.

FIG. 18 shows Cassini curves from a ninety 100-μs pulse IRE treatmentthat represent the average zone of ablation (blue dashed), +SD (redsolid), and −SD (black solid) according to a=0.821±0.062 andb=1.256±0.079.

FIG. 19 is a representation of the Finite Element Analysis (FEA) modelfor a 3D Electric Field [V/cm] Distribution in Non-Electroporated(Baseline) Tissue with 1.5-cm Electrodes at a Separation of 2.0 cm andwith 3000 V applied.

FIGS. 20A-D are representations of the Electric Field [V/cm]Distributions from the 3D Non-Electroporated (Baseline) Models of FIG.19 , wherein FIG. 20A represents the x-y plane mid-electrode length,FIG. 20B represents the x-z plane mid-electrode diameter, FIG. 20Crepresents the y-z plane mid-electrode diameter, and FIG. 20D representsthe y-z plane between electrodes.

FIG. 21 is a representation of the Finite Element Analysis (FEA) modelfor a 3D Electric Field [V/cm] Distribution in Electroporated Tissuewith 1.5-cm Electrodes at a Separation of 2.0 cm and 3000 V appliedassuming σ_(max)/σ₀=3.6.

FIGS. 22A-22D are representations of the Electric Field [V/cm]Distributions from the 3D Electroporated Models with 1.5-cm Electrodesat a Separation of 2.0 cm and 3000 V (cross-sections) assumingσ_(max)/σ₀=3.6, wherein FIG. 22A represents the x-y plane mid-electrodelength, FIG. 22B represents the x-z plane mid-electrode diameter, FIG.22C represents the y-z plane mid-electrode diameter, and FIG. 22Drepresents the y-z plane between electrodes.

FIG. 23 is a representative Cassini curve representing zones of ablationderived using the pre-pulse procedure to determine the ratio of maximumconductivity to baseline conductivity. For comparison purposes thebaseline electric field isocontour is also presented in which noelectroporation is taken into account.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

Reference will now be made in detail to various exemplary embodiments ofthe invention. Embodiments described in the description and shown in thefigures are illustrative only and are not intended to limit the scope ofthe invention. Changes may be made in the specific embodiments describedin this specification and accompanying drawings that a person ofordinary skill in the art will recognize are within the scope and spiritof the invention.

Throughout the present teachings, any and all of the features and/orcomponents disclosed or suggested herein, explicitly or implicitly, maybe practiced and/or implemented in any combination, whenever andwherever appropriate as understood by one of ordinary skill in the art.The various features and/or components disclosed herein are allillustrative for the underlying concepts, and thus are non-limiting totheir actual descriptions. Any means for achieving substantially thesame functions are considered as foreseeable alternatives andequivalents, and are thus fully described in writing and fully enabled.The various examples, illustrations, and embodiments described hereinare by no means, in any degree or extent, limiting the broadest scopesof the claimed inventions presented herein or in any future applicationsclaiming priority to the instant application.

One embodiment of the present invention is illustrated in FIGS. 1 and 2. Representative components that can be used with the present inventioncan include one or more of those that are illustrated in FIG. 1 . Forexample, in embodiments, one or more probes 22 can be used to delivertherapeutic energy and are powered by a voltage pulse generator 10 thatgenerates high voltage pulses as therapeutic energy such as pulsescapable of irreversibly electroporating the tissue cells. In theembodiment shown, the voltage pulse generator 10 includes six separatereceptacles for receiving up to six individual probes 22 which areadapted to be plugged into the respective receptacle. The receptaclesare each labeled with a number in consecutive order. In otherembodiments, the voltage pulse generator can have any number ofreceptacles for receiving more or less than six probes.

For example, a treatment protocol according to the invention couldinclude a plurality of electrodes. According to the desired treatmentpattern, the plurality of electrodes can be disposed in variouspositions relative to one another. In a particular example, a pluralityof electrodes can be disposed in a relatively circular pattern with asingle electrode disposed in the interior of the circle, such as atapproximately the center. Any configuration of electrodes is possibleand the arrangement need not be circular but any shape periphery can beused depending on the area to be treated, including any regular orirregular polygon shape, including convex or concave polygon shapes. Thesingle centrally located electrode can be a ground electrode while theother electrodes in the plurality can be energized. Any number ofelectrodes can be in the plurality such as from about 1 to 20. Indeed,even 3 electrodes can form a plurality of electrodes where one groundelectrode is disposed between two electrodes capable of being energized,or 4 electrodes can be disposed in a manner to provide two electrodepairs (each pair comprising one ground and one electrode capable ofbeing energized). During treatment, methods of treating can involveenergizing the electrodes in any sequence, such as energizing one ormore electrode simultaneously, and/or energizing one or more electrodein a particular sequence, such as sequentially, in an alternatingpattern, in a skipping pattern, and/or energizing multiple electrodesbut less than all electrodes simultaneously, for example.

In the embodiment shown, each probe 22 includes either a monopolarelectrode or bipolar electrodes having two electrodes separated by aninsulating sleeve. In one embodiment, if the probe includes a monopolarelectrode, the amount of exposure of the active portion of the electrodecan be adjusted by retracting or advancing an insulating sleeve relativeto the electrode. See, for example, U.S. Pat. No. 7,344,533, which isincorporated by reference herein in its entirety. The pulse generator 10is connected to a treatment control computer 40 having input devicessuch as keyboard 12 and a pointing device 14, and an output device suchas a display device 11 for viewing an image of a target treatment areasuch as a lesion 300 surrounded by a safety margin 301. The therapeuticenergy delivery device 22 is used to treat a lesion 300 inside a patient15. An imaging device 30 includes a monitor 31 for viewing the lesion300 inside the patient 15 in real time. Examples of imaging devices 30include ultrasonic, CT, MRI and fluoroscopic devices as are known in theart.

The present invention includes computer software (treatment planningmodule 54) which assists a user to plan for, execute, and review theresults of a medical treatment procedure, as will be discussed in moredetail below. For example, the treatment planning module 54 assists auser to plan for a medical treatment procedure by enabling a user tomore accurately position each of the probes 22 of the therapeutic energydelivery device 20 in relation to the lesion 300 in a way that willgenerate the most effective treatment zone. The treatment planningmodule 54 can display the anticipated treatment zone based on theposition of the probes and the treatment parameters. The treatmentplanning module 54 can display the progress of the treatment in realtime and can display the results of the treatment procedure after it iscompleted. This information can be displayed in a manner such that itcan be used for example by a treating physician to determine whether thetreatment was successful and/or whether it is necessary or desirable tore-treat the patient.

For purposes of this application, the terms “code”, “software”,“program”, “application”, “software code”, “computer readable code”,“software module”, “module” and “software program” are usedinterchangeably to mean software instructions that are executable by aprocessor. The “user” can be a physician or other medical professional.The treatment planning module 54 executed by a processor outputs variousdata including text and graphical data to the monitor 11 associated withthe generator 10.

Referring now to FIG. 2 , the treatment control computer 40 of thepresent invention manages planning of treatment for a patient. Thecomputer 40 is connected to the communication link 52 through an I/Ointerface 42 such as a USB (universal serial bus) interface, whichreceives information from and sends information over the communicationlink 52 to the voltage generator 10. The computer 40 includes memorystorage 44 such as RAM, processor (CPU) 46, program storage 48 such asROM or EEPROM, and data storage 50 such as a hard disk, all commonlyconnected to each other through a bus 53. The program storage 48 stores,among others, a treatment planning module 54 which includes a userinterface module that interacts with the user in planning for, executingand reviewing the result of a treatment. Any of the software programmodules in the program storage 48 and data from the data storage 50 canbe transferred to the memory 44 as needed and is executed by the CPU 46.

In one embodiment, the computer 40 is built into the voltage generator10. In another embodiment, the computer 40 is a separate unit which isconnected to the voltage generator through the communications link 52.In a preferred embodiment, the communication link 52 is a USB link. Inone embodiment, the imaging device 30 is a standalone device which isnot connected to the computer 40. In the embodiment as shown in FIG. 1 ,the computer 40 is connected to the imaging device 30 through acommunications link 53. As shown, the communication link 53 is a USBlink. In this embodiment, the computer can determine the size andorientation of the lesion 300 by analyzing the data such as the imagedata received from the imaging device 30, and the computer 40 candisplay this information on the monitor 11. In this embodiment, thelesion image generated by the imaging device 30 can be directlydisplayed on the grid (not shown) of the display device (monitor) 11 ofthe computer running the treatment planning module 54. This embodimentwould provide an accurate representation of the lesion image on thegrid, and may eliminate the step of manually inputting the dimensions ofthe lesion in order to create the lesion image on the grid. Thisembodiment would also be useful to provide an accurate representation ofthe lesion image if the lesion has an irregular shape.

It should be noted that the software can be used independently of thepulse generator 10. For example, the user can plan the treatment in adifferent computer as will be explained below and then save thetreatment parameters to an external memory device, such as a USB flashdrive (not shown). The data from the memory device relating to thetreatment parameters can then be downloaded into the computer 40 to beused with the generator 10 for treatment. Additionally, the software canbe used for hypothetical illustration of zones of ablation for trainingpurposes to the user on therapies that deliver electrical energy. Forexample, the data can be evaluated by a human to determine or estimatefavorable treatment protocols for a particular patient rather thanprogrammed into a device for implementing the particular protocol.

FIG. 3 illustrates one embodiment of a circuitry to detect anabnormality in the applied pulses such as a high current, low current,high voltage or low voltage condition. This circuitry is located withinthe generator 10 (see FIG. 1 ). A USB connection 52 carries instructionsfrom the user computer 40 to a controller 71. The controller can be acomputer similar to the computer 40 as shown in FIG. 2 . The controller71 can include a processor, ASIC (application-specific integratedcircuit), microcontroller or wired logic. The controller 71 then sendsthe instructions to a pulse generation circuit 72. The pulse generationcircuit 72 generates the pulses and sends electrical energy to theprobes. For clarity, only one pair of probes/electrodes are shown.However, the generator 10 can accommodate any number ofprobes/electrodes (e.g., from 1-10, such as 6 probes) and energizingmultiple electrodes simultaneously for customizing the shape of theablation zone. In the embodiment shown, the pulses are applied one pairof electrodes at a time, and then switched to another pair. The pulsegeneration circuit 72 includes a switch, preferably an electronicswitch, that switches the probe pairs based on the instructions receivedfrom the computer 40. A sensor 73 such as a sensor can sense the currentor voltage between each pair of the probes in real time and communicatesuch information to the controller 71, which in turn, communicates theinformation to the computer 40. If the sensor 73 detects an abnormalcondition during treatment such as a high current or low currentcondition, then it will communicate with the controller 71 and thecomputer 40 which may cause the controller to send a signal to the pulsegeneration circuit 72 to discontinue the pulses for that particular pairof probes. The treatment planning module 54 can further include afeature that tracks the treatment progress and provides the user with anoption to automatically retreat for low or missing pulses, orover-current pulses (see discussion below). Also, if the generator stopsprematurely for any reason, the treatment planning module 54 can restartat the same point where it terminated, and administer the missingtreatment pulses as part of the same treatment. In other embodiments,the treatment planning module 54 is able to detect certain errors duringtreatment, which include, but are not limited to, “charge failure”,“hardware failure”, “high current failure”, and “low current failure”.

General treatment protocols for the destruction (ablation) ofundesirable tissue through electroporation are known. They involve theinsertion (bringing) electroporation electrodes to the vicinity of theundesirable tissue and in good electrical contact with the tissue andthe application of electrical pulses that cause irreversibleelectroporation of the cells throughout the entire area of theundesirable tissue. The cells whose membrane was irreversiblepermeabilized may be removed or left in situ (not removed) and as suchmay be gradually removed by the body's immune system. Cell death isproduced by inducing the electrical parameters of irreversibleelectroporation in the undesirable area.

Electroporation protocols involve the generation of electrical fields intissue and are affected by the Joule heating of the electrical pulses.When designing tissue electroporation protocols it is important todetermine the appropriate electrical parameters that will maximizetissue permeabilization without inducing deleterious thermal effects. Ithas been shown that substantial volumes of tissue can be electroporatedwith reversible electroporation without inducing damaging thermaleffects to cells and has quantified these volumes (Davalos, R. V., B.Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effectsduring in vivo tissue electroporation. Bioelectrochemistry, 2003. Vol.61(1-2): p. 99-107).

The electrical pulses used to induce irreversible electroporation intissue are typically larger in magnitude and duration from theelectrical pulses required for reversible electroporation. Further, theduration and strength of the pulses for irreversible electroporation aredifferent from other methodologies using electrical pulses such as forintracellular electro-manipulation or thermal ablation. The methods arevery different even when the intracellular (nano-seconds)electro-manipulation is used to cause cell death, e.g. ablate the tissueof a tumor or when the thermal effects produce damage to cells causingcell death.

Typical values for pulse length for irreversible electroporation are ina range of from about 5 microseconds to about 62,000 milliseconds orabout 75 microseconds to about 20,000 milliseconds or about 100microseconds±10 microseconds. This is significantly longer than thepulse length generally used in intracellular (nano-seconds)electro-manipulation which is 1 microsecond or less—see published U.S.application 2002/0010491 published Jan. 24, 2002.

The pulse is typically administered at voltage of about 100 V/cm to7,000 V/cm or 200 V/cm to 2000 V/cm or 300V/cm to 1000 V/cm about 600V/cm for irreversible electroporation. This is substantially lower thanthat used for intracellular electro-manipulation which is about 10,000V/cm, see U.S. application 2002/0010491 published Jan. 24, 2002.

The voltage expressed above is the voltage gradient (voltage percentimeter). The electrodes may be different shapes and sizes and bepositioned at different distances from each other. The shape may becircular, oval, square, rectangular or irregular etc. The distance ofone electrode to another may be 0.5 to 10 cm, 1 to 5 cm, or 2-3 cm. Theelectrode may have a surface area of 0.1-5 sq. cm or 1-2 sq. cm.

The size, shape and distances of the electrodes can vary and such canchange the voltage and pulse duration used. Those skilled in the artwill adjust the parameters in accordance with this disclosure to obtainthe desired degree of electroporation and avoid thermal damage tosurrounding cells.

Additional features of protocols for electroporation therapy areprovided in U.S. Patent Application Publication No. US 2007/0043345 A1,the disclosure of which is hereby incorporated by reference in itsentirety.

The present invention provides systems and methods for estimating a3-dimensional treatment volume for a medical treatment device thatapplies treatment energy through a plurality of electrodes defining atreatment area. The systems and methods are based in part on calculationof the ratio of a maximum conductivity of the treatment area to abaseline conductivity of the treatment area, and may be used todetermine effective treatment parameters for electroporation-basedtherapies. The present inventors have recognized that the baseline andmaximum conductivities of the tissue should be determined before thetherapy in order to determine safe and effective pulse protocols.

The numerical models and algorithms of the invention, as provided in theExamples, such as Equation 3 of Example 1 can be implemented in a systemfor estimating a 3-dimensional treatment volume for a medical treatmentdevice that applies treatment energy through a plurality of electrodesdefining a treatment area. In one embodiment, the numerical models andalgorithms are implemented in an appropriate computer readable code aspart of the treatment planning module 54 of the system of the invention.Computing languages available to the skilled artisan for programming thetreatment planning module 54 include general purpose computing languagessuch as the C and related languages, and statistical programminglanguages such as the “S” family of languages, including R and S-Plus.The computer readable code may be stored in a memory 44 of the system ofthe invention. A processor 46 is coupled to the memory 44 and a displaydevice 11 and the treatment planning module 54 stored in the memory 44is executable by the processor 46. The treatment planning module 54,through the implemented numerical models, is adapted to generate anestimated first 3-dimensional treatment volume for display in thedisplay device 11 based on the ratio of a maximum conductivity of thetreatment area to a baseline conductivity of the treatment area (Z).

In one embodiment, the invention provides for a system for estimating a3-dimensional treatment volume for a medical treatment device thatapplies treatment energy through a plurality of electrodes 22 defining atreatment area, the system comprising a memory 44, a display device 11,a processor 46 coupled to the memory 44 and the display device 11, and atreatment planning module 54 stored in the memory 44 and executable bythe processor 46, the treatment planning module 54 adapted to generatean estimated first 3-dimensional treatment volume for display in thedisplay device 11 based on the ratio of a maximum conductivity of thetreatment area to a baseline conductivity of the treatment area.

The foregoing description provides additional instructions andalgorithms for a computer programmer to implement in computer readablecode a treatment planning module 54 that may be executable through aprocessor 46 to generate an estimated 3-dimensional treatment volume fordisplay in the display device 11 based on the ratio of a maximumconductivity of the treatment area to a baseline conductivity of thetreatment area.

The treatment planning module 54 may derive the baseline conductivityand maximum conductivity of the treatment area based on a relationshipof current as a function of W, X, and Y, in which:

W=voltage to distance ratio;

X=edge to edge distance between electrodes; and

Y=exposure length of electrode.

The treatment planning module 54 may derive the baseline conductivityusing a pre-treatment pulse.

The treatment planning module 54 may generate the estimated first3-dimensional treatment volume using a numerical model analysis such asdescribed in the Examples. The numerical model analysis may includefinite element analysis (FEA).

The treatment planning module 54 may generate the estimated first3-dimensional treatment volume using a set of second 3-dimensionalablation volumes according to different W, X, Y and Z values, which havebeen predetermined by the numerical model analysis.

The treatment planning module 54 may generate the estimated first3-dimensional treatment volume using a set of second 3-dimensionalablation volumes according to different W, X, Y and Z values, which havebeen pre-determined by a numerical model analysis; and generating a setof interpolated third 3-dimensional volumes based on the predeterminedset of second 3-dimensional ablation volumes.

The treatment planning module 54 may derive by curve fitting: amathematical function of x values of the ablation volume as a functionof any one or more of W, X, Y and/or Z; a mathematical function of yvalues of the ablation volume as a function of any one or more of W, X,Y and/or Z; and/or a mathematical function of z values of the ablationvolume as a function of any one or more of W, X, Y and/or Z.

The treatment planning module 54 may generate the estimated first3-dimensional treatment volume using the three mathematical functions.

The treatment planning module 54 may: measure a baseline and maximumconductivity of the treatment area; generate a fourth 3-dimensionaltreatment volume based on the measured baseline and maximumconductivity; and optionally display one or both the first and fourth3-dimensional treatment volumes in the display device 11.

The treatment planning module 54 may superimpose one of the first andfourth 3-dimensional treatment volumes over the other so as to enable aphysician to compare an estimated result to an actual estimated result.

In another embodiment, the invention provides a system for estimating atarget ablation zone for a medical treatment device that applieselectrical treatment energy through a plurality of electrodes 22defining a target treatment area, the system comprising a memory 44, adisplay device 11, a processor 46 coupled to the memory 44 and thedisplay device 11; and a treatment planning module 54 stored in thememory 44 and executable by the processor 46, the treatment planningmodule 54 adapted to receive a baseline electrical flow characteristic(EFC) in response to delivery of a test signal to tissue of a subject 15to be treated, determine a second EFC representing an expected EFCduring delivery of the electrical treatment energy to the targettreatment area, and estimating the target ablation zone for display inthe display device 11 based on the second EFC. The EFC may include anelectrical conductivity.

The second EFC may include a maximum conductivity expected during thedelivery of the electrical treatment energy to the target treatmentarea; and the treatment planning module estimates the target ablationzone based on the ratio of the second EFC to the baseline EFC.

The treatment planning module 54 may estimate the second EFC to be amultiple of the baseline EFC which is greater than 1 and less than 6.

The treatment planning module 54 may estimate the second EFC to be amultiple of the baseline EFC which is greater than 3 and less than 4.

The treatment planning module 54 may deliver the test signal thatincludes a high frequency AC signal in the range of 500 kHz and 10 MHz.

The treatment planning module 54 may deliver the test signal thatincludes an excitation AC voltage signal of 1 to 10 mV, such as from 1mV to 125 V, including for example from about 1 to 5 V, or from about10-50 V, or from about 100-125 V.

The treatment planning module may deliver the test signal that includesa low voltage non-electroporating pre-IRE pulse of 10 V/cm to 100 V/cm.

The treatment planning module may deliver the test signal that includesa low voltage non-electroporating pre-IRE pulse of 25 V/cm to 75 V/cm.

The treatment planning module 54 may deliver the test signal thatincludes the high frequency AC signal and a DC pulse.

The treatment planning module 54 may determines a third EFC thatrepresents an actual EFC during delivery of the electrical treatmentenergy for confirmation of the estimated target ablation zone.

The treatment planning module 54 may determine the second EFC based onW, X and Y, in which: W=voltage to distance ratio; X=edge to edgedistance between electrodes; Y=exposure length of electrode.

The treatment planning module 54 may be operably configured to estimatethe target ablation zone based on a set of predetermined ablation zonesaccording to different W, X, Y and Z values.

The treatment planning module may estimate the target ablation zone bycurve fitting: a mathematical function of x values of the ablationvolume as a function of any one or more of W, X, Y and/or Z; amathematical function of y values of the ablation volume as a functionof any one or more of W, X, Y and/or Z; and/or a mathematical functionof z values of the ablation volume as a function of any one or more ofW, X, Y and/or Z.

The treatment planning module 54 is programmed to execute the algorithmsdisclosed herein through the processor 46. In one embodiment, thetreatment planning module 54 is programmed to execute the followingalgorithm 1000, as shown in FIG. 4 , in computer readable code throughthe processor 46:

Initiating a low voltage pre-IRE pulse through a probe 1100;

Measuring the current of the low voltage pre-IRE pulse through probe1200;

Optionally, scaling the current measured in step 1200 to match avoltage-to-distance ratio value 1300;

Solving 1400 for factor in the following equation provided in Example 1to determine the baseline electric conductivityI=factor·[aW+bX+cY+dZ+e(W−W )(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]

Providing at least one high voltage IRE pulse through the probe toprovide an IRE treatment 1500;

Providing a low voltage post-IRE pulse through the probe 1600;

Measuring the current of the low voltage post-IRE pulse through probe1700;

Optionally, scaling the current measured in step 1700 to match avoltage-to-distance value 1800;

Solving 1900 for factor in the following equation provided in Example 1to determine the maximum electric conductivity post-IREI=factor·[aW+bX+cY+dZ+e(W−W )(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]

Generating an estimated first 3-dimensional treatment volume based onthe ratio of the maximum conductivity of the treatment area to thebaseline conductivity of the treatment area 2000.

The steps in the algorithm 1000 shown in FIG. 4 need not be followedexactly as shown. For example, it may be desirable to eliminate one orboth scaling steps 1300, 1800. It may also be desirable to introduce orsubstitute steps, such as, for example, providing a mathematicalfunction of x, y, z values of the 3-dimensional treatment volume as afunction of any one or more of W, X, Y, and/or Z by curve fitting, andestimating the 3-dimensional treatment volume using the threemathematical functions, or introducing additional steps disclosedherein.

For example, specific method embodiments of the invention include amethod for estimating a target ablation zone for a medical treatmentdevice that applies electrical treatment energy through a plurality ofelectrodes defining a target treatment area, the method comprising:determining a baseline electrical flow characteristic (EFC) in responseto delivery of a test signal to tissue of a subject to be treated;determining, based on the baseline EFS, a second EFC representing anexpected EFC during delivery of the electrical treatment energy to thetarget treatment area; and estimating the target ablation zone fordisplay in the display device based on the second EFC.

Such methods can include where the step of determining a baseline EFCincludes determining an electrical conductivity.

Additionally or alternatively, such methods can include where the stepof determining a second EFC includes determining an expected maximumelectrical conductivity during delivery of the electrical treatmentenergy to the target treatment area; and the step of estimating includesestimating the target ablation zone based on the ratio of the second EFCto the baseline EFC.

Even further, the treatment planning module in method and systemembodiments can estimate the second EFC to be a multiple of the baselineEFC which is greater than 1 and less than 6. For example, the treatmentplanning module can estimate the second EFC to be a multiple of thebaseline EFC which is greater than 3 and less than 4.

Methods of the invention are provided wherein the treatment planningmodule delivers the test signal that includes a high frequency AC signalin the range of 500 kHz and 10 MHz. Alternatively or in addition methodscan include wherein the treatment planning module delivers the testsignal that includes the high frequency AC signal and a DC pulse.

In method embodiments of the invention, the treatment planning moduledetermines a third EFC that represents an actual EFC during delivery ofthe electrical treatment energy for confirmation of the estimated targetablation zone.

Methods of the invention can comprise displaying results of treatment ina manner which indicates whether treatment was successful or whetherfurther treatment is needed. Method steps can include further deliveringelectrical treatment energy to a target tissue or object in response todata obtained in the determining and/or estimating steps of methods ofthe invention.

According to embodiments, a method is provided for estimating a targetablation zone, the method comprising: determining a baseline electricalflow characteristic (EFC) in response to delivery of a test signal to atarget area of an object; determining, based on the baseline EFS, asecond EFC representing an expected EFC during delivery of theelectrical treatment energy to the target area; estimating the targetablation zone for display in the display device based on the second EFC.For example, according to such methods the object can be a biologicalobject, such as tissue, a non-biological object, such as a phantom, orany object or material such as plant material.

Systems and methods of the invention can comprise a treatment planningmodule adapted to estimate the target ablation zone based in part onelectrode radius and/or a step of estimating the target ablation zonebased in part on electrode radius.

In embodiments of the methods, the treatment planning module determinesthe second EFC based on W, X and Y, in which: W=voltage to distanceratio; X=edge to edge distance between electrodes; and Y=exposure lengthof electrode.

The treatment planning module of method embodiments can estimate thetarget ablation zone based on a set of predetermined ablation zonesaccording to different W, X and Y values.

Method embodiments further include that the treatment planning moduleestimates the target ablation zone by curve fitting: a mathematicalfunction of x values of the ablation volume as a function of any one ormore of W, X and/or Y; a mathematical function of y values of theablation volume as a function of any one or more of W, X and/or Y; and amathematical function of z values of the ablation volume as a functionof any one or more of W, X and/or Y.

The system may be further configured to include software for displayinga Graphical User Interface in the display device with various screensfor input and display of information, including those for Information,Probe Selection, Probe Placement Process, and Pulse Generation asdescribed in International Patent Application Publication WO 2010/117806A1, the disclosure of which is hereby incorporated by reference in itsentirety.

Additional details of the algorithms and numerical models disclosedherein will be provided in the following Examples, which are intended tofurther illustrate rather than limit the invention.

In Example 1, the present inventors provide a numerical model that usesan asymmetrical Gompertz function to describe the response of porcinerenal tissue to electroporation pulses. However, other functions couldbe used to represent the electrical response of tissue under exposure topulsed electric fields such as a sigmoid function, ramp, and/orinterpolation table. This model can be used to determine baselineconductivity of tissue based on any combination of electrode exposurelength, separation distance, and non-electroporating electric pulses. Inaddition, the model can be scaled to the baseline conductivity and usedto determine the maximum electric conductivity after theelectroporation-based treatment. By determining the ratio ofconductivities pre- and post-treatment, it is possible to predict theshape of the electric field distribution and thus the treatment volumebased on electrical measurements. An advantage of this numerical modelis that it is easy to implement in computer software code in the systemof the invention and no additional electronics or numerical simulationsare needed to determine the electric conductivities. The system andmethod of the invention can also be adapted for other electrodegeometries (sharp electrodes, bipolar probes), electrode diameter, andother tissues/tumors once their response to different electric fieldshas been fully characterized.

The present inventors provide further details of this numerical modelingas well as experiments that confirm this numerical modeling in Example2. In developing this work, the present inventors were motivated todevelop an IRE treatment planning method and system that accounts forreal-time voltage/current measurements. As a result of this work, thesystem and method of the invention requires no electronics or electrodesin addition to the NANOKNIFE® System, a commercial embodiment of asystem for electroporation-based therapies. The work shown in Example 2is based on parametric study using blunt tip electrodes, but can becustomized to any other geometry (sharp, bipolar). The numericalmodeling in Example 2 provides the ability to determine a baselinetissue conductivity based on a low voltage pre-IRE pulse(non-electroporating ˜50 V/cm), as well as the maximum tissueconductivity based on high voltage IRE pulses (during electroporation)and low voltage post-IRE pulse (non-electroporating ˜50 V/cm). Twonumerical models were developed that examined 720 or 1440 parametercombinations. Results on IRE lesion were based on in vitro measurements.A major finding of the modeling in Example 2 is that the electric fielddistribution depends on conductivity ratio pre- and post-IRE.Experimental and clinical IRE studies may be used to determine thisratio. As a result, one can determine e-field thresholds for tissue andtumor based on measurements. The 3-D model of Example 2 captures depth,width, and height e-field distributions.

In Example 3, as a further extension of the inventors work, theinventors show prediction of IRE treatment volume based on 1000 V/cm,750 v/cm, and 500 V/cm IRE thresholds as well as other factors as arepresentative case of the numerical modeling of the invention.

In Example 4, the inventors describe features of the SpecificConductivity and procedures for implementing it in the invention.

In Example 5, the inventors describe in vivo experiments as a reductionto practice of the invention.

In Example 6, the inventors describe how to use the ratio of maximumconductivity to baseline conductivity in modifying the electric fielddistribution and thus the Cassini oval equation.

In Example 7, the inventors describe the Cassini oval equation and itsimplementation in the invention.

EXAMPLES Example 1

Materials and Methods

The tissue was modeled as a 10-cm diameter spherical domain using afinite element package (Comsol 4.2a, Stockholm, Sweden). Electrodes weremodeled as two 1.0-mm diameter blunt tip needles with exposure lengths(Y) and edge-to-edge separation distances (X) given in Table 1. Theelectrode domains were subtracted from the tissue domain, effectivelymodeling the electrodes as boundary conditions.

TABLE 1 Electrode configuration and relevant electroporation- basedtreatment values used in study. PARAMETER VALUES MEAN W [V/cm] 500,1000, 1500, 2000, 1750 2500, 3000 X [cm] 0.5, 1.0, 1.5, 2.0, 2.5 1.5 Y[cm] 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 1.75 Z [cm] 1.0, 1.25, 1.5, 2.0, 3.0,2.96875 4.0, 5.0, 6.0

The electric field distribution associated with the applied pulse isgiven by solving the Laplace equation:∇·(σ(|E|)∇φ)=0  (1)

where σ is the electrical conductivity of the tissue, E is the electricfield in V/cm, and φ is the electrical potential (Edd and Davalos,2007). Boundaries along the tissue in contact with the energizedelectrode were defined as φ=V_(o), and boundaries at the interface ofthe other electrode were set to ground. The applied voltages weremanipulated to ensure that the voltage-to-distance ratios (W)corresponded to those in Table 1. The remaining boundaries were treatedas electrically insulating, ∂φ/∂n=0.

The analyzed domain extends far enough from the area of interest (i.e.the area near the electrodes) that the electrically insulatingboundaries at the edges of the domain do not significantly influence theresults in the treatment zone. The physics-controlled finer mesh with˜100,000 elements was used. The numerical models have been adapted toaccount for a dynamic tissue conductivity that occurs as a result ofelectroporation, which is described by an asymmetrical Gompertz curvefor renal porcine tissue (Neal et al., 2012):σ(|E|)=σ_(o)+(σ_(max)−σ_(o))exp[−A·exp[−B·E]  (2)

where σ_(o) is the non-electroporated tissue conductivity and σ_(max) isthe maximum conductivity for thoroughly permeabilized cells, A and B arecoefficients for the displacement and growth rate of the curve,respectively. Here, it is assumed that σ₀=0.1 S/m but this value can bescaled by a factor to match any other non-electroporated tissueconductivity or material as determined by a pre-treatment pulse. In thiswork the effect of the ratio of maximum conductivity to baselineconductivity in the resulting electric current was examined using the50-μs pulse parameters (A=3.05271; B=0.00233) reported by Neal et al.(Neal et. al., 2012). The asymmetrical Gompertz function showing thetissue electric conductivity as a function of electric field is forexample shown in FIG. 5 .

The current density was integrated over the surface of the groundelectrode to determine the total current delivered. A regressionanalysis on the resulting current was performed to determine the effectof the parameters investigated and their interactions using theNonlinearModelFit function in Wolfram Mathematica 8.0. Current data fromthe numerical simulations were fit to a mathematical expression thataccounted for all possible interactions between the parameters:I=factor·[aW+bX+cY+dZ+e(W−WW)(X−X )+f(W−W )(Y−Y )+g(W−W )(Z−Z )+h(X−X)(Y−Y )+i(X−X )(Z−Z )+j(Y−Y )(Z−Z )+k(W−W )(X−X )(Y−Y )+l(X−X )(Y−Y)(Z−Z )+m(W−W )(Y−Y )(Z−Z )+n(W−W )(X−X )(Z−Z )+o(W−W )(X−X )(Y−Y )(Z−Z)+p]  (3)

where I is the current in amps, W is the voltage-to-distance ratio[V/cm], X is the edge-to-edge distance [cm], Y is the exposure length[cm], and Z is the unitless ratio σ_(max)/σ_(o). The W, X, Y, and Z aremeans for each of their corresponding parameters (Table 1) and thecoefficients (a, b, c, . . . , n, o, p) were determined from theregression analysis (Table 2).

Results.

A method to determine electric conductivity change following treatmentbased on current measurements and electrode configuration is provided.The best-fit statistical (numerical) model between the W, X, Y, and Zparameters resulted in Eqn. 3 with the coefficients in Table 2(R²=0.999646). Every coefficient and their interactions had statisticalsignificant effects on the resulting current (P<0.0001*). With thisequation one can predict the current for any combination of the W, Y, X,Z parameters studied within their ranges (500 V/cm W 3000 V/cm, 0.5cm≤X≤2.5 cm, 0.5 cm≤Y≤3.0 cm, and 1.0≤Z≤6.0). Additionally, by using thelinear results (Z=1), the baseline tissue conductivity can beextrapolated for any blunt-tip electrode configuration by delivering andmeasuring the current of a non-electroporating pre-treatment pulse. Thetechniques described in this specification could also be used todetermine the conductivity of other materials, such as non-biologicalmaterials, or phantoms.

TABLE 2 Coefficients (P < 0.0001*) from the Least Square analysis usingthe NonlinearModelFit function in Mathematica. ESTIMATE a → 0.00820 b →7.18533 c → 5.80997 d → 3.73939 e → 0.00459 f → 0.00390 g → 0.00271 h →3.05537 i → 2.18763 j → 1.73269 k → 0.00201 l → 0.92272 m → 0.00129 n →0.00152 o → 0.00067 p → −33.92640

FIG. 6 shows a representative case in which the effect of the W and Zare studied for electroporation-based therapies with 2.0 cm electrodesseparated by 1.5 cm. The 3D plot corroborates the quality of the modelwhich shows every data point from the numerical simulation (greenspheres) being intersected by the best-fit statistical (numerical)model. This 3D plot also shows that when Z is kept constant, the currentincreases linearly with the voltage-to-distance ratio (W). Similarly,the current increases linearly with Z when the voltage-to-distance ratiois constant. However, for all the other scenarios there is a non-linearresponse in the current that becomes more drastic with simultaneousincreases in Wand Z.

In order to fully understand the predictive capability of thestatistical (numerical) model, two cases in which the current ispresented as a function of the exposure length and electrode separationare provided. FIG. 7A shows the linear case (Z=1) in which the currentcan be scaled to predict any other combination of pulse parameters aslong as the pulses do not achieve electroporation. For example, one candeliver a non-electroporation pulse (˜50 V/cm) and measure current. Thecurrent can then be scaled to match one of the W values investigated inthis study. By using Eqn. 3 and solving for the factor, the baselineelectric conductivity of the tissue can be determined and used fortreatment planning. FIG. 7B is the case in which the maximum electricconductivity was 0.4 S/m (Z=4) after electroporation. The trends aresimilar to the ones described in FIG. 5 in that if exposure length isconstant, the current increases linearly with increasing electrodeseparation and vice versa. However, even though the conductivity withinthe treated region increases by a factor of 4, the current increasesnon-linearly only by a factor of 3. This can be seen by comparing thecontours in FIG. 7A with those in FIG. 7B which consistently show thatthe curves are increased by a factor of 3.

Example 2. Determining the Relationship Between Blunt Tip ElectrodeConfiguration and Resulting Current after IRE Treatment

Model Assumptions:

Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue

Baseline Conductivity: σ=0.1 S/m

Spherical Domain: diameter=10 cm

Applied Voltage: Voltage=1000 V

Parametric Study:

Total Combinations: 720 models

Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline

Edge-to-edge Distance: 5, 10, 15, 20, 25 mm

Electrode Exposure: 5, 10, 15, 20, 25, 30 mm

Electrode Radius: 0.5, 0.75, 1.0 mm

The output of statistical analysis software (JMP 9.0) used to fit modeland determine the coefficients for all parameter combinations is shownin the tables of FIGS. 8A and 8B and the plot of FIG. 8C.

Parameters of Best Fit for Dynamic Conductivity Changes Between 1×-6×the Baseline Conductivity (R²=0.96):

a=−1.428057; (*Intercept Estimate*)

b=−0.168944; (*Gap Estimate*)

c=2.1250608; (*Radius Estimate*)

d=0.2101464; (*Exposure Estimate*)

e=1.1114726; (*Factor Estimate*)

f=−0.115352; (*Gap-Radius Estimate*)

g=−0.010131; (*Gap-Exposure Estimate*)

h=−0.067208; (*Gap-Factor*)

i=0.0822932; (*Radius-Exposure Estimate*)

j=0.4364513; (*Radius-Factor Estimate*)

k=0.0493234; (*Exposure-Factor Estimate*)

l=−0.006104; (*Gap-Radius-Exposure Estimate*)

m=0.0165237; (*Radius-Exposure-Factor Estimate*)*)

n=−0.003861; (*Gap-Exposure-Factor Estimate*)

o=−0.041303; (*Gap-Radius-Factor Estimate*)

p=−0.002042; (*Gap-Radius-Exposure-Factor Estimate*)

Analytical Function for Dynamic Conductivity Changes Between 1×-6× theBaseline Conductivity (R²=0.96):

5 mm<gap=x<25 mm, 0.5 mm<radius=y<1.0 mm,

5 mm<exposure=z<30 mm, 1<factor=w<6

Default conductivity of 0.1 S/m and 1000 V which can be scaled fordynamic conductivities. The function is a linear combination of alliterations examined in the parametric study:Current(w,x,y,z)=a+bx+cy+dz+ew+f(x+bb)(y+cc)+g(x+bb)(z+dd)+h(x+bb)(w+ee)+i(y+cc)(z+dd)+j(y+cc)(w+ee)+k(z+dd)(w+ee)+l(x+bb)(y+cc)+m(y+cc)(z+dd)(w+ee)+n(x+bb)(z+dd)(w+ee)+o(x+bb)(y+cc)(w+ee)+p(x+bb)(y+cc)(z+dd)(w+ee)

FIGS. 9A-9F show the representative (15 mm gap) correlation betweencurrent vs. exposure length and electrode radius for maximumconductivities (1×-6 x, respectively).

FIGS. 10A and 10B are tables showing experimental validation of the codefor determining the tissue/potato dynamic conductivity from in vitromeasurements.

Determining the Relationship Between Blunt Tip Electrode Configurationand e-Field Distribution after IRE Treatment

Model Assumptions:

Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue

Baseline Conductivity: a=0.1 S/m

Spherical Domain: diameter=10 cm

Electrode Radius: r=0.5 mm

Parametric Study:

Total Combinations: 1440 models

Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline

Edge-to-edge Distance: 5, 10, 15, 20, 25 mm

Electrode Exposure: 5, 10, 15, 20, 25, 30 mm

Voltage-to-distance Ratio: 500, 1000, 1500, 2000, 2500, 3000 V/cm

Example 3

Comparison of analytical solutions with statistical (numerical) model tocalculate current and explanation of procedure that results in 3D IREvolume.

The process of backing-out the electrical conductivity using theanalytical solutions and the one proposed in the “Towards a PredictiveModel of Electroporation-Based Therapies using Pre-Pulse ElectricalMeasurements” abstract presented in the IEEE Engineering in Medicine andBiology Conference in Aug. 28, 2012 in San Diego, Calif. were compared.A method to determine the predictive power of the equations to calculatecurrent is analyzing the residuals of the 1440 combinations ofparameters examined. In the context of this specification, a residual isthe difference between the predicted current and the actual current. Ascan be seen in FIGS. 11A and 11B with increasing non-linear change inconductivity due to electroporation and increasing applied electricfield there is an increase in the residual for both cases. The mainmessage though is that using the shape factor (analytical) method themaximum residual is 11.3502 A and with the statistical (numerical) modelthe maximum is 1.55583 A. This analysis suggests that the shape factormethod may be inadequate to predict the non-linear changes in currentthat occur during electroporation and for reliable predictions thestatistical (numerical) method may be better.

In terms of the prediction of the volume treated a representative methodis to map out the electric field 5 cm in the directions along the(x,0,0), (0,y,0), and (0,0,z) axes from the origin. In addition, theelectric field can be extracted along a line that starts at the originand ends at 3 cm along each of the axes. These plots contain theinformation for determining the distances at which a particular IREthreshold occurs. In embodiments, 1440 different parameter combinationswere simulated that resulted in data sets of 28,692 (x-direction),20,538 (y-direction), 27,306 (z-direction), and 25,116 (xyz-direction)for homogeneous conductivity. Even though these simulations only includedynamic conductivity changes due to electroporation, it is believed thatan identical analysis for simulations that also include the changes inconductivity due to temperature could also be performed. In this manner,it would be possible to determine irreversible electroporationthresholds as a function of temperature and electroporation.Manipulating these large data sets is challenging but it provides allthe necessary information to study the effect of electrode separation,electrode length, dynamic conductivity factor, and voltage-to-distanceratio for any position along the described paths. In order to be able tomanipulate the data and extract the distance for different IREthresholds, the function NonlinearModelFit (Mathematica) was used inorder to come up with analytical expressions that would closely matchthe electric field. A different function was used for each of thedirections studied in the positive directions along the Cartesiancoordinate system. The Micheilis Menten function was used along thex-direction (R²=0.978978), the analytical solution to the Laplaceequation along the y-direction (R²=0.993262), and the Logistic equationin the z-direction (R²=0.983204). Each of those functions was scaled bya 3rd order polynomial function that enabled the fit to incorporate theelectrode separation and electrode exposure as well. Even though thedescribed functions were used to fit the data from the numerical data,there might be other functions that are also appropriate and this willbe explored further in order to use the most reliable fit. In FIGS.12A-12C provided are representative contour plots of the electric fieldstrength at 1.0 cm from the origin using an edge-to-edgevoltage-to-distance ratio of 1500 V/cm assuming a z=1 which is the casefor non-electroporated electrical conductivity. It is important to notethat in this case the y and z data are starting from (0, 0, 0) and thex-data starts outside the external electrode-tissue boundary. Onerepresentative case is presented, but any of the 1440 parameterscombinations that were disclosed in the conference proceeding could beplotted as well.

The following functions describe the electric field [V/cm] distributionsalong the x-axis (E_(x)), y-axis (E_(y)), and z-axis (E_(z)) as afunction of voltage-to-distance (W), edge-to-edge separation between theelectrodes (X), exposure length (Y), maximum conductivity to baselineconductivity (Z), and distance in the x-direction (xx), y-direction(yy), and z-direction (zz).

Micheilis Menten Equation (Electric Field in the x-Direction)E _(x)(W,X,Y,Z,xx)=W*(a*Exp[−b·xx]+c)*(dX ³ eX ² fX+gY ³ +hY ² +iY+j)+k

The coefficients for the NonlinearModelFit are given below:

a=−0.447392, b=8.98279, c=−0.0156167, d=−0.0654974, e=0.468234,f=−6.17716, g=0.326307, h=−2.33953, I=5.90586, j=−4.83018, k −9.44083

Laplace  Equation  (electric  field  in  the  y-direction)${E_{y}\left( {W,X,Y,Z,{yy}} \right)} = {\alpha + {\left( {X^{3} + X^{2} + {bX} + {cY}^{3} + {dY}^{2} + {eY} + f} \right)*\left( {h + {\frac{({gWXZ})}{2}*\left( \frac{1}{\left. {{Log}\left\lbrack \frac{X + 0.1}{0.05} \right\rbrack} \right)*} \right)*{{Abs}\left\lbrack {\frac{1}{{{\mathbb{i}} \cdot {yy}} - \frac{X}{2} - 0.05} - \frac{1}{{{\mathbb{i}} \cdot {yy}} + \frac{X}{2} + 0.05}} \right\rbrack}}} \right)}}$

The coefficients for the NonlinearModelFit are given below:

a=−56.6597, b=−42.9322, c=6.66389, d=−50.8391, e=141.263, f=138.934,g=0.00417123, h=0.184109

Laplace  Equation  (electric  field  in  the  z-direction)${E_{z}\left( {W,X,Y,Z,{zz}} \right)} = {a + {\frac{bWZ}{1 + {c \cdot {{Exp}\left\lbrack {d \cdot \left( {\frac{2\;{zz}}{y} - e} \right)} \right\rbrack}}} \cdot \left( {{fX}^{3} + {gX}^{2} + {hX} + i} \right) \cdot \left( {{jY}^{3} + {kY}^{2} + {lY} + m} \right)}}$

The coefficients for the NonlinearModelFit are given below:

a=49.0995, b=−0.00309563, c=1.39341, d=4.02546, e=1.24714, f=0.276404,g=−1.84076, h=4.93473, I=−9.13219, j=0.699588, k=−5.0242, l=12.8624,m=19.9113.

In order to visualize the predicted IRE shape the equation of anellipsoid was used and the semi-axes were forced to intersect with thelocations at which the IRE threshold wants to be examined. Therefore,the provided functions can be adjusted in real-time to display the IREvolume for any electric field threshold. This is important sincedifferent tissues have different IRE thresholds that depend on thetemperature, dielectric properties of the tissue, the electrodeconfiguration, and the pulse parameters used. Once again, even thoughthe equation for an ellipsoid is used to represent the IRE volume, otherfunctions may be evaluated that may also be appropriate to replicate themorphology of the zones of ablation being achieved experimentally suchas the Cassini curve. A 1500 V/cm was used as the voltage-to-distanceratio, electrode exposure 2 cm, and electrode separation 1.5 cm togenerate 3 different IRE zones using 1000 V/cm, 750 V/cm, and 500 V/cmas the IRE thresholds with z=1.

From the 3D plots representing the zones of ablation shown in FIGS.13A-13C it can be seen that if the IRE threshold is reduced from 1000V/cm to either 750 V/cm or 500 V/cm, the volume becomes larger. This isrepresentative of how different tissues may have different thresholdsand this code may provide the ability to simulate the fields in abroad/generic manner that can then be applied to any tissue.Incorporating the xyz-data that was extracted from the parametric studywill help modify the “roundness” of the current depictions of the zoneof IRE ablation in order to more realistically replicate theexperimental results. However, to the best of the inventors' knowledgethere is no such adaptable code currently available to provide a 3D IREvolume as a function of measured current, electrode length, electrodeexposure, applied voltage-to-distance ratio, and customizable electricfield threshold so it is believed that this will greatly help themedical community in planning and verifying the clinical treatments ofpatients being treated with the IRE technology.

Example 4

Specific Conductivity

Specific conductivity can be important in embodiments for treatmentplanning of irreversible electroporation (IRE). For many applications,especially when treating tumors in the brain, the volume (area) of IREshould be predicted to maximize the ablation of the tumorous tissuewhile minimizing the damage to surrounding healthy tissue. The specificelectrical conductivity of tissue during an irreversible electroporation(IRE) procedure allows the physicians to: determine the currentthreshold; minimize the electric current dose; decrease the Jouleheating; and reduce damage to surrounding healthy tissue. To measure thespecific conductivity of tissue prior to an IRE procedure the physiciantypically performs one or more of the following: establishes theelectrode geometry (shape factor); determines the physical dimensions ofthe tissue; applies a small excitation AC voltage signal (1 to 10 mV);measures the AC current response; calculates the specific conductivity(a) using results from the prior steps. This procedure tends to notgenerate tissue damage (low amplitude AC signals) and will supply thephysician (software) with the required information to optimize IREtreatment planning, especially in sensitive organs like the brain whichis susceptible to high electrical currents and temperatures. Thus, theIRE procedure is well monitored and can also serve as a feedback systemin between series of pulses and even after the treatment to evaluate thearea of ablation.

Special Cases for electrode geometry

Nomenclature (units in brackets):

V_(e)=voltage on the hot electrode (the highest voltage), [V]

G=electroporation voltage gradient (required for electroporation), [V/m]

R₁=radius of electrode with highest voltage (inner radius), [m]

R₂=radius at which the outer electrodes are arranged (outer radius), [m]

i=total current, [A]

L=length of cylindrical electrode, [m]

A=area of plate electrode, [m²]

σ=electrical conductivity of tissue, [S/m]

ρ=density

c=heat capacity

Case 1

Electrical conduction between a two-cylinder (needle) arrangement oflength L in an infinite medium (tissue). It is important to note thatthis formulation is most accurate when L>>R₁,R₂ and L>>w. The electricalconductivity can be calculated from,

$\sigma = \frac{i \cdot S}{V_{e}}$

where the shape factor (S) corresponding to the electrode dimensions andconfiguration is given by,

$\frac{2 \cdot \pi \cdot L}{\cosh^{- 1}\left( \frac{{4 \cdot w^{2}} - \left( {2 \cdot R_{1}} \right)^{2} - \left( {2 \cdot R_{2}} \right)^{2}}{8 \cdot R_{1} \cdot R_{2}} \right)}$

Case 2

Cylindrical arrangement in which the central electrode is a cylinder(needle) with radius R₁ and the outer electrodes are arranged in acylindrical shell with a shell radius of R₂ (not the radius of theelectrodes). The voltage on the central electrode is V_(e). The voltagedistribution in the tissue may be determined as a function of radius, r:

$V = {V_{e}\frac{\ln\;\frac{r}{R_{2}}}{\ln\;\frac{R_{1}}{R_{2}}}}$

The required voltage on the central electrode to achieve IRE:

$V_{e} = {{GR}_{2}\ln\frac{R_{2}}{R_{1}}}$

The required current on the central electrode:

$i = \frac{2\pi\; L\;\sigma\; V_{e}}{\ln\frac{R_{2}}{R_{1}}}$

The specific conductivity (σ) of the tissue can be calculated since thevoltage signal (V_(e)) and the current responses (i) are known.

Explanation of electrical concepts.

By using the bipolar electrode described previously in US PatentApplication Publication No. 2010/0030211 A1, one can apply a smallexcitation AC voltage signal (for example from about 1 to 10 mV),V(t)=V ₀ Sin(ωt)

where V(t) is the potential at time t, V₀ is the amplitude of theexcitation signal and ω is the frequency in radians/s. The reason forusing a small excitation signal is to get a response that ispseudo-linear since in this manner the value for the impedance can bedetermined indicating the ability of a system (tissue) to resist theflow of electrical current. The measured AC current (response) that isgenerated by the excitation signal is described byI(t)=I ₀ Sin(ωt+θ)

where I (t) is the response signal, I₀ is the amplitude of the response(I₀≠V₀) and θ is the phase shift of the signal. The impedance (Z) of thesystem (tissue) is described by,Z=(V(t))/I(t))=(V ₀ Sin(ωt))/(I ₀ Sin(ωt+θ))=Z ₀(Sin(ωt))/(Sin(ωt+θ))

It is important to note that the measurement of the response is at thesame excitation frequency as the AC voltage signal to preventinterfering signals that could compromise the results. The magnitude ofthe impedance |Z₀| is the electrical resistance of the tissue. Theelectrical resistivity (Ω m) can be determined from the resistance andthe physical dimensions of the tissue in addition to the electrodegeometry (shape factor). The reciprocal of the electrical resistivity isthe electrical conductivity (S/m). Therefore, after deriving theelectrical resistivity from the methods described above, theconductivity may be determined.

As described in U.S. Patent Application No. 61/694,144 the analyticalsolution (Table 4) assumes that the length of the electrodes is muchlarger than the electrode radius or separation distance between theelectrodes. Additionally, the analytical solution is not capable ofcapturing the non-linear electrical response of the tissue duringelectroporation procedures. The proposed statistical algorithm (Table 3)is preferably used in order to capture the response in treatments thatare being conducted clinically and show how the analytical overestimatesthe baseline and maximum current that uses the experimental data.

TABLE 3 Determination of conductivity using the statistical model and invivo data from pre-pulse and IRE pulses in canine kidney tissue usingidentical electrode configuration that the experimental one describedbelow. Current Voltage Volt-2-Dist Conductivity Z = [A] [V] [V/cm] [S/m]σ_(max)/σ_(min) Pre-Pulse 0.258 48 53 0.365 — IRE-Pulse 20.6 1758 19531.037 2.841 IRE-Pulse 23.7 1758 1953 1.212 3.320 IRE-Pulse 23.6 17581953 1.207 3.305 Avg. IRE 22.6 1758 1953 1.150 3.150 IRE-Pulse 10.4 12591399 0.727 1.990 IRE-Pulse 11.1 1257 1397 0.789 2.162 IRE-Pulse 11 12571397 0.781 2.138 Avg. IRE 10.8 1257 1397 0.763 2.090 Pre-Pulse 0.34373.3 52 0.341 — IRE-Pulse 23.6 2262 1616 1.007 2.952 IRE-Pulse 24.3 22621616 1.041 3.051 IRE-Pulse 25.4 2262 1616 1.094 3.207 Avg. IRE 24.5 22621616 1.050 3.080

TABLE 4 Determination of conductivity using the analytical model and invivo data from pre-pulse and IRE pulses in canine kidney tissue usingidentical electrode configuration than the experimental one describedbelow. Assumption: Length >> radius, Length >> width, 2 cylindricalelectrodes in an infinite medium. Current Voltage Volt-2-Dist ShapeFactor Conductivity [A] [V] [V/cm] [m] [S/m] Pre-Pulse 0.258 48 530.01050 0.512 IRE-Pulse 20.6 1758 1953 0.01050 1.116 IRE-Pulse 23.7 17581953 0.01050 1.284 IRE-Pulse 23.6 1758 1953 0.01050 1.279 Avg. IRE 22.61758 1953 0.01050 1.225 IRE-Pulse 10.4 1259 1399 0.01050 0.787 IRE-Pulse11.1 1257 1397 0.01050 0.841 IRE-Pulse 11 1257 1397 0.01050 0.834 Avg.IRE 10.8 1257 1397 0.01050 0.819 Pre-Pulse 0.343 73.3 52 0.00924 0.506IRE-Pulse 23.6 2262 1616 0.00924 1.129 IRE-Pulse 24.3 2262 1616 0.009241.163 IRE-Pulse 25.4 2262 1616 0.00924 1.215 Avg. IRE 24.5 2262 16160.00924 1.172

Example 5

In Vivo Experiments

1) Animals.

IRE ablations were performed in canine kidneys in a procedure approvedby the local animal ethics committee. Male canines weighingapproximately 30 kg were premedicated with acetylpromazine (0.1 mg/kg),atropine (0.05 mg/kg), and morphine (0.2 mg/kg) prior to generalanesthesia induced with propofol (6 mg/kg, then 0.5 mg/kg/min) andmaintained with inhaled isofluorane (1-2%). Anesthetic depth wasmonitored by bispectral index monitoring (Covidien, Dublin, Ireland) ofEEG brain activity. After ensuring adequate anesthesia, a midlineincision was made and mesenchymal tissue was maneuvered to access thekidney. Pancuronium was delivered intravenously to mitigate electricallymediated muscle contraction, with an initial dose of 0.2 mg/kg, andadjusted if contractions increased.

2) Experimental Procedure.

Two modified 18 gauge needle electrodes (1.0 mm diameter and 1.0 cm inexposure) were inserted as pairs into the superior, middle, or inferiorlobe of the kidney, with lobes being randomly selected. A BTX ECM830pulse generator (Harvard Apparatus, Cambridge, Mass.) was used todeliver an initial 100 μs pre-pulse of 50 V/cm voltage-to-distance ratio(center-to-center) between the electrodes to get an initial current ableto be used to determine baseline conductivity. Electrical current wasmeasured with a Tektronix TCP305 electromagnetic induction current probeconnected to a TCPA300 amplifier (both Tektronix, Beaverton, Oreg.). AProtek DSO-2090 USB computer-interface oscilloscope provided currentmeasurements on a laptop using the included DSO-2090 software (both GSInstruments, Incheon, Korea). A schematic of the experimental setup canbe found in FIG. 14A. Following the pre-pulse, a series of 100 pulses,each 100 μs long, at a rate of 1 pulse per second was delivered,reversing polarity after 50 pulses. A five second pause was encounteredafter pulses 10 and 50 to save data. A schematic diagram showingdimension labeling conventions is shown in FIG. 14B. Representativecurrent waveforms from a pre-pulse and experimental pulse can be foundin FIGS. 14C and 14D, respectively. Electrode exposure lengths were setto 1 cm for all trials. The separation distance between electrodes andapplied voltage may be found in Table 5. After completing pulsedelivery, the electrodes were removed. Two additional ablations wereperformed in the remaining lobes before repeating the procedure on thecontralateral kidney, resulting in a total of three ablations per kidneyand six per canine.

TABLE 5 KIDNEY EXPERIMENT PROTOCOLS IN CANINE SUBJECTS Voltage-Separation, Voltage, Distance Setup cm V Ratio, V/cm n 1 1 1250 1250 4 21 1750 1750 4 3 1.5 2250 1500 6

3) Kidney Segmentation and 3D Reconstruction.

Numerical models provide an advantageous platform for predictingelectroporation treatment effects by simulating electric field,electrical conductivity, and temperature distributions. By understandingthe electric field distribution, one can apply an effective lethalelectric field threshold for IRE, EIRE, to predict ablation lesiondimensions under varying pulse protocols (electrode arrangements andapplied voltages). However, in order to do so, these models should firstbe calibrated with experimental data. Here, the numerical simulationalgorithm developed from porcine kidneys was expanded that accounts forconductivity changes using an asymmetrical sigmoid function (R. E. Neal,2nd, et al., “Experimental characterization and numerical modeling oftissue electrical conductivity during pulsed electric fields forirreversible electroporation treatment planning,” IEEE Trans BiomedEng., vol. 59, pp. 1076-85. Epub 2012 Jan. 6, 2012 (“R. E. Neal, 2^(nd),et al., 2012”)). The model is calibrated to the experimental lesions todetermine an effective electric field threshold under the threeexperimental setups used. In addition, static and linear conductivityfunctions are also correlated to the lesion dimensions. The threefunctions are used to evaluate which numerical technique will result inbetter accuracy in matching lesion shapes and resulting current fromactual IRE ablations in mammalian tissue, particularly for kidney.

The imaging-based computational model domains were constructed from amagnetic resonance imaging (MRI) scan of a kidney from a canine subjectof similar size to those in the study. The scans were scaled by 1.21times in all directions to better match the experimental kidneydimensions while maintaining the anatomical characteristics. Mimics 14.1image analysis software (Materialise, Leuven, BG) was used to segmentthe kidney geometry from the surrounding tissues. The kidney was tracedin each of the two-dimensional (2D) MRI axial slices, which were thenintegrated into a three-dimensional (3D) solid representation of thekidney volume which was refined and exported to 3-matic version 6.1(Materialise, Leuven, BG) to generate a volumetric mesh compatible withComsol Multiphysics finite element modeling software (ComsolMultiphysics, v.4.2a, Stockholm, Sweden).

Electrodes were simulated as paired cylinders, each 1 cm long and 1 mmin diameter, and separated by 1 or 1.5 cm to represent the twoexperimental conditions. The pairs were inserted into the 3D kidney meshin two configurations, representing both experimental approaches thatused either the superior/inferior (vertical) or middle (horizontal) lobeof the kidney, both with tips 1.5 cm deep. The finite element modelsimulated the electric field distribution in the kidney, which was usedto determine cell death EIRE by correlating the electric field valueswith the average in vivo lesion height and width dimensions.

4) Electric Field Distribution and Lethal EIRE Determination.

The electric field distribution is determined according to−∇·(σ(|E|)∇ϕ)=0  (1)

where σ is the electrical conductivity of the tissue, E is the electricfield in V/cm, and ϕ is the electrical potential. Tissue-electrodeboundaries for the cathode and anode were defined as ϕ=V_(o) and ground,respectively. The remaining boundaries were treated as electricallyinsulating, dϕ/dn=0, since the kidneys were isolated from thesurrounding mesenchymal tissue during the experimental procedures. Thecurrent density was integrated over a mid-plane parallel to bothelectrodes to determine simulated electric current.

The model was solved for the vertical and horizontal electrodeconfigurations, each considering three electrical conductivity tissueresponses. These responses included a homogeneous static conductivity(σ₀) as well as two that accounted for electroporation basedconductivity changes in tissue that result from cell membranepermeabilization. The dynamic models are based on a relationship betweena minimum baseline and a maximum conductivity. The static conductivitymodel was used to determine the baseline conductivity, σ₀, by matchingsimulated electrical current with the pre-pulse experimental data, wherethe field strength should be below that able to permeabilize any cellsin the tissue. The maximum conductivity, Amax, occurs when the number ofcells electroporated in the tissue has saturated, and the cellularmembranes no longer restrict the extent of interstitial electrolytemobility. The statistical model discussed in (P. A. Garcia, et al.,“Towards a predictive model of electroporation-based therapies usingpre-pulse electrical measurements,” Conf Proc IEEE Eng Med Biol Soc,vol. 2012, pp. 2575-8, 2012 (“P. A. Garcia, et al., 2012”)) was used topredict σ_(max) from previously characterized tissue response topre-pulse σ₀ and electrical data.

The σ₀ and σ_(max) values provide the required parameters to define theelectric field-dependent conductivity, σ(|E|), of renal tissue in vivo.One model assumed a linear relationship that grew between the minimumand maximum conductivities over a range from 200 to 2000 V/cm,σ_(L)(|E|), and the second used an asymmetrical sigmoid Gompertz curve,σ_(S)(|E|), derived from the work described in (R. E. Neal, 2nd, et al.,2012) using the equation:σ_(s)(|E|)=σ₀+(σ_(max)−σ₀)·exp[−A·exp(−B·E)](2)

where A and B are unitless coefficients that vary with pulse length, t(s). This function was fit using curve parameters for a 100 μs longpulse, where A=3.053 and B=0.00233 (R. E. Neal, 2^(nd), et al., 2012)

The electric field distribution along a width and height projectionbased at the midpoint length of the electrodes was used to determine theelectric field magnitude that matched experimental lesion dimensions.This was performed for all three conductivity scenarios in all threeexperimental protocol setups in order to determine which model bestmatched the IRE ablations, providing the optimum conductivity modelingtechnique for mammalian tissue.

5) Results: In Vivo Experiments.

Electrical Currents.

All animals survived the procedures without adverse event untileuthanasia. Electrical pre-pulse currents were 0.258±0.036 A (mean±SD)for the 1 cm electrode separation trials and 0.343±0.050 A for the 1.5cm separation trials. Electrical currents from the trials for pulses1-10, 40-50, and 90-100 are reported in Table 6. Although currents aretypically reported to increase with consecutive pulses, there is nostatistically significant correlation between pulse number and measuredcurrent. Therefore, all numerical calibrations to match electricalcurrent and determine σ_(max) used the average current from all capturedpulses for each experimental setup.

TABLE 6 EXPERIMENTAL ELECTRIC CURRENTS TO CALIBRATE NUMERICAL MODELSAverage Separation, Delivered Pulse Average Electric Setup cm Voltage, VNumber Current, A* Pre 1 1 48 1750 0.258 (0.036) Pre 2 1.5 73 1250 0.343(0.050) 1 1 1258 1-10 10.4 (1.7) 40-50  11.1 (1.1) 90-100 11.0 (1.7) 2 21758 1-10 20.6 (3.2) 40-50  23.7 (5.1) 90-100 23.6 (3.8) 3 1.5 2262 1-1023.6 (1.47) 40-50  24.3 (3.25) 90-100 25.4 (3.27) *Currents given as“average (standard deviation)”

6) Determination of Dynamic Conductivity Function.

Pre-pulse electrical current was used to calculate the baselineconductivity, σ₀, used in the static numerical simulation. In addition,the baseline and maximum, σ_(max), electrical conductivities requiredfor generating the asymmetrical sigmoid and linear dynamic conductivityfunctions were calculated according to the procedure outlined in (P. A.Garcia, et al., 2012) and are provided in Table 7. The ratio betweenthese conductivities was calculated and demonstrates an increase inconductivity between 2.09 and 3.15 times, consistent with valuesdetermined in the literature for other organs (N. Payselj, et al., “Thecourse of tissue permeabilization studied on a mathematical model of asubcutaneous tumor in small animals,” IEEE Trans Biomed Eng, vol. 52,pp. 1373-81, August 2005).

TABLE 7 BASELINE AND MAXIMUM ELECTRIC CONDUCTIVITIES Gap, V/d Ratio,Setup cm V/cm σ₀ σ_(max) σ_(max)/σ₀ 1 1 1250 0.365 0.763 2.09 2 1 17500.365 1.150 3.15 3 1.5 1500 0.341 1.050 3.08

Example 6

How to Use the Ratio of Maximum Conductivity to Baseline Conductivity inModifying the Electric Field Distribution and Thus the Cassini OvalEquation.

Irreversible electroporation (IRE) is a promising new method for thefocal ablation of undesirable tissue and tumors. The minimally invasiveprocedure involves placing electrodes into the region of interest anddelivering a series of low energy electric pulses to induceirrecoverable structural changes in cell membranes, thus achievingtissue death. To achieve IRE, the electric field in the region ofinterest needs to be above a critical threshold, which is dependent on avariety of conditions such as the physical properties of the tissue,electrode geometry and pulse parameters. Additionally, the electricconductivity of the tissue changes as a result of the pulses,redistributing the electric field and thus the treatment area. Theeffect of a dynamic conductivity around the electrodes where the highestelectric fields are generated was investigated in order to betterpredict the IRE treatment for clinical use.

The electric field distribution associated with the electric pulse isgiven by solving the governing Laplace equation, ∇·(σ∇φ)=0, where σ isthe tissue electrical conductivity (baseline 0.2 S/m) and φ theelectrical potential (3000 V). The dynamic changes in electricalconductivity due to electroporation were modeled with the flc2hsHeaviside function within the finite element modeling software used inthe study (Comsol Multiphysics 3.5a, Stockholm, Sweden). The dynamicconductivity factor ranged between 2.0-7.0 times the baseline value inthe regions exceeding 3000 V/cm. The total electrical current, volumes,and lesion shapes from the IRE treatment were evaluated.

FIGS. 15A and 15B display the electric field distributions for thenon-electroporated (baseline conductivity) and electroporated(maximum/baseline conductivity) maps, respectively. The electric fieldfrom using the baseline conductivity resulted in a “peanut” shapedistribution (FIG. 15A). By incorporating the conductivity ratio betweenσ_(max)/σ₀, there is a redistribution of the electric field and thus thevolumes, currents and lesion shapes are modified as well. The electricfield distribution for a 7.0× factor (FIG. 15B), shows a more gradualdissipation of the electric field and a rounder predicted IRE lesion.

A method to predict IRE lesions and incorporate the dynamic changes inconductivity due to electroporation around the electrodes is presentedin this example. This procedure provides additional tools to betterapproximate the electric field distributions in tissue and thus help togenerate more reliable IRE treatment planning for clinical use usingFinite Element Analysis (FEA) models.

Specifically in order to adapt the Cassini Oval to match experimentallesions or electric field distributions the following procedure shouldbe used:

In IRE treatments, the electric field distribution is the primary factorfor dictating defect formation and the resulting volume of treatedtissue (J. F. Edd and R. V. Davalos, “Mathematical modeling ofirreversible electroporation for treatment planning,” Technol Cancer ResTreat, vol. 6, pp. 275-286, 2007; D. Sel, et al., “Sequential finiteelement model of tissue electropermeabilization,” IEEE Trans Biomed Eng,vol. 52, pp. 816-27, May 2005; S. Mahnic-Kalamiza, et al., “Educationalapplication for visualization and analysis of electric field strength inmultiple electrode electroporation,” BMC Med Educ, vol. 12, p. 102, 2012(“S. Mahnic-Kalamiza, et al., 2012”)). The electric field is influencedby both the geometry and positioning of the electrodes as well as thedielectric tissue properties. Additionally, altered membranepermeability due to electroporation influences the tissue conductivityin a non-linear manner. Therefore numerical techniques are preferablyused to account for different electrode configurations and incorporatetissue-specific functions relating the electrical conductivity to theelectric field distribution (i.e. extent of electroporation). Theinventors are currently using imaging-based computational models for IREtreatment planning that use the physical properties of the tissue andpatient-specific 3D anatomical reconstructions to generate electricfield distributions (P. A. Garcia, et al., “Non-thermal irreversibleelectroporation (N-TIRE) and adjuvant fractionated radiotherapeuticmultimodal therapy for intracranial malignant glioma in a caninepatient,” Technol Cancer Res Treat, vol. 10, pp. 73-83, 2011 (“P. A.Garcia, et al, 2011”)).

Oftentimes in clinical practice, there is need to rapidly visualize theestimated zone of ablation without relying in complex and time consumingnumerical simulations. As an alternative, analytical solutions arepowerful techniques that provide valuable insight and offer the abilityto rapidly visualize electric field distributions (S. Mahnic-Kalamiza,et al., 2012). However, these analytical solutions assume infinitelylong electrodes which are not the case in clinical practice and do notincorporate the non-linear changes in tissue conductivity due toelectroporation. Therefore, there is a need for simple, quick, andaccurate methods to provide physicians with predicted IRE zones ofablation during surgery when one of the pulse parameters needs to beadjusted. To this end, the inventors have adapted the Cassini curve inan effort to provide researchers and physicians with a graphicalrepresentation of IRE zones of ablation, for example, in in vivo porcineliver. The goal of this work is to provide a correlation betweenexperimentally produced zones of ablations in in vivo porcine livertissue with the corresponding IRE pulse parameters and electrodeconfiguration. These Cassini curves are calibrated to experimental IREablations, and incorporate the dynamic changes in tissue conductivity, alimitation of the analytical approach.

The Cassini oval is a plane curve that derives its set of values basedon the distance of any given point, a, from the fixed location of twofoci, q₁ and q₂, located at (x₁, y₁) and (x₂, y₂). The equation issimilar to that of an ellipse, except that it is based on the product ofdistances from the foci, rather than the sum. This makes the equationfor such an oval└(x ₁ −a)²+(y ₁ −a)²┘·└(x ₂ −a)²+(y ₂ −a)² ┘=b ⁴  (3)

where b⁴ is a scaling factor to determine the value at any given point.For incorporation of this equation into shapes that mimic the electricfield distribution, it is assumed that the two foci were equidistantlylocated on the x-axis at (±x,0). The flexibility of the Cassini curve iscrucial since it allows for fitting a wide range of shapes by adjustingthe ‘a’ and/or ‘b’ parameters from Equation 3 simultaneously and fittingthem to the experimental lesion dimensions or the locations at which aparticular electric field value results from the computationalsimulations. The new approach in this analysis is that it is not assumedthat the parameter ‘a’ is related to the separation distance between theelectrodes used in IRE treatments for example but will be a secondparameter to match the width/depth of any distribution thus allowing formore flexibility between the shapes achieved with the Cassini Oval ascan be seen in FIGS. 16A and 16B.

The in vivo experimental data in porcine liver was provided frompublished studies performed at the Applied Radiology Laboratory ofHadassah Hebrew University Medical Center (P. A. Garcia, et al., 2011).All experiments were performed with Institutional Animal Care and UseCommittee approval from the Hebrew University Medical Center. Thetreatments were performed with a two-needle electrode configuration, 1.5cm center-to-center separation, 2.0 cm electrode exposure, and anapplied voltage of 2250 V. In this paper we only evaluate the effect ofpulse number and pulse duration on the resulting ‘a’ and ‘b’ parametersrequired to fit the IRE zones of ablation with the Cassini curve. TheNonlinearModelFit function in Wolfram Mathematica 9 was used todetermine the ‘a’ and ‘b’ parameters (average±standard deviation) foreach pulse parameter resulting in three curves for each condition. Thissame technique can be used to fit the ‘a’ and ‘b’ parameters to matchthe electric field shape at any particular electric field value as wellthus providing an avenue to capture the shape for any IRE lesionindependent of the tissue or patient.

The NonlinearModelFit results for the ‘a’ and ‘b’ parameters to generatethe Cassini curves are provided in FIG. 17 . The ‘a’ parameter rangedfrom 0.75-1.04 and the ‘b’ from 1.06-1.35 for the average IRE zones ofablation in the in vivo porcine liver. From these data it can be seenthat each pulse parameter used results in a unique ‘a’ and ‘b’combination except for the twenty 100-μs pulses and ninety 20-μs pulseswhich overlap since they had identical IRE ablations. Therefore,consideration should be given to pulse length and total number of pulseswhen planning treatments to ensure maximum accuracy when using Cassinicurves to rapidly predict treatment zones.

FIG. 18 provides a representation of the average IRE zone of ablationand also includes the experimentally achieved standard deviations. ThisCassini curve is the most clinically relevant as ninety 100-μs pulses isthe recommended setting by the manufacturer that is currently being usedby physicians to treat several types of cancer. The Cassini curves inFIG. 18 were generated with a=0.821±0.062 and b=1.256±0.079 thatcorresponded to IRE ablations that were 3.0±0.2 cm in width and 1.9±0.1cm in depth (P. A. Garcia, et al., 2011). The results suggest that theCassini curve is a viable method to represent experimentally achievedIRE zones of ablation. These curves can be used to provide physicianswith simple, quick, and accurate prediction of IRE treatments. Theparameters generated in this study were achieved from porcine liverablations data. Therefore, future work needs to determine the parametersfor other tissues and/or tumors. Cassini curve parameters should bere-calibrated if the pulse parameters or electrode configuration (i.e.separation or exposure) deviate from the typical protocols in Ben-Davidet al. Additionally, there is a need to calibrate these Cassini curvesto electric and temperature distributions in order to take advantage ofthe relatively simple curves in representing simulated solutions thataccount for other pulse parameters and electrode configuration includingdifferent electrode separations, diameter, exposure, and voltages. Amethod to represent IRE zones of ablation in a computationally efficientmanner and based on experimental data is thus presented. Such methodscan be used to predict IRE ablation in liver in order to providephysicians with an immediate tool for treatment planning.

FIG. 19 is a representation of the 3D Electric Field [V/cm] Distributionin Non-Electroporated (Baseline) Tissue with 1.5-cm Electrodes at aSeparation of 2.0 cm and 3000 V applied.

FIGS. 20A-D are representations of the Electric Field [V/cm]Distributions from the 3D Non-Electroporated (Baseline) Models with1.5-cm Electrodes at a Separation of 2.0 cm and 3000 V (cross-sections),wherein FIG. 20A is a representation of the x-y plane mid-electrodelength, FIG. 20B is a representation of the x-z plane mid-electrodediameter, FIG. 20C is a representation of the y-z plane mid electrodediameter, and FIG. 20D is a representation of the y-z plane betweenelectrodes.

FIG. 21 is a representation of the 3D Electric Field [V/cm] Distributionin Electroporated Tissue with 1.5-cm Electrodes at a Separation of 2.0cm and 3000 V applied assuming σ_(max)/σ₀=3.6.

FIGS. 22A-22D are representations of the Electric Field [V/cm]Distributions from the 3D Electroporated Models with 1.5-cm Electrodesat a Separation of 2.0 cm and 3000 V (cross-sections) assumingσ_(max)/σ₀=3.6, wherein FIG. 22A is a representation of the x-y planemid-electrode length, FIG. 22B is a representation of the x-z planemid-electrode diameter, FIG. 22C is a representation of the y-z planemid electrode diameter, and FIG. 22D is a representation of the y-zplane between electrodes.

Example 7. The Cassini Oval Equation

In mathematics, a Cassini oval is a set (or locus) of points in theplane such that each point p on the oval bears a special relation to twoother, fixed points q₁ and q₂: the product of the distance from p to q₁and the distance from p to q₂ is constant. That is, if the functiondist(x,y) is defined to be the distance from a point x to a point y,then all points p on a Cassini oval satisfy the equation:dist(q ₁ ,p)×dist(q ₂ ,p)=b ²  (2)

-   -   where b is a constant.

Nevertheless, in embodiments the ‘b’ parameter can be modified tomanipulate the shape of the Cassini curve and illustrate the desiredelectric field distribution. Therefore, the ‘b’ is a variable parameterthat is determined based on the specific location (distance) of aparticular electric field threshold to be displayed.

The points q₁ and q₂ are called the foci of the oval.

Suppose q₁ is the point (a,0), and q₂ is the point (−a,0). Then thepoints on the curve satisfy the equation:((x−a)² +y ²)((x+a)² +y ²)=b ⁴  (3)

The equivalent polar equation is:r ⁴−2a ² r ² cos 2θ=b ⁴ −a ⁴  (4)

The shape of the oval depends on the ratio b/a. When b/a is greater than1, the locus is a single, connected loop. When b/a is less than 1, thelocus comprises two disconnected loops. When b/a is equal to 1, thelocus is a lemniscate of Bernoulli.

The Cassini equation provides a very efficient algorithm for plottingthe boundary line of the treatment zone that was created between twoprobes on grid 200. By taking pairs of probes for each firing sequence,the first probe is set as qi being the point (a,0) and the second probeis set as q₂ being the point (−a,0). This original Cassini ovalformulation was revised by modifying the assumption of the ‘a’ parameterbeing related to the position of the electrodes. In the revisedformulation the ‘a’ is a variable parameter that is adjusted dependingon the width and length of the Cassini oval in order to intercept thezone of ablation in the x- and y-directions.

In summary, the ‘a’ and ‘b’ variable parameters should be determined inorder to have the ability to generate a Cassini curve that could fit theshape of any electric field isocontour. Specifically from the electricfield simulations or experimental irreversible electroporation zones ofablation the user should determine the distance along the x-axis andy-axis that the Cassini curve should intersect.

For example in the case of a Finite Element Analysis (FEA) simulationusing two 1-mm in diameter electrodes, separated by a center-to-centerdistance of 2.0 cm, 1.5 cm in exposure, and an applied voltage of 3000 Vto one electrode and ground to the other electrode the distances fromthe point in between the electrodes to a specific electric field contouris given below (Table 8 for the baseline (non-electroporated) andσ_(max)/σ₀=3.6 (electroporated) models.

TABLE 8 E-field Baseline Baseline σ_(max)/σ₀ = 3.6 σ_(max)/σ₀ = 3.6[V/cm] (p_(1x), 0) [cm] (0, p_(2y)) [cm] (p_(3x), 0) [cm] (0, p_(4y))[cm] 300 1.97 0.92 2.38 1.39 400 1.81 0.69 2.17 1.18 500 1.70 0.49 1.991.01

Using the 500 V/cm electric field isocontour as an example it can bedetermined that the Cassini oval using the baseline model will intersectthe points (1.70,0) and (0,0.49) and the model using σ_(max)/σ₀=3.6 willintersect the point (1.99,0) and (0,1.01). Using the two points thatwill be intersected by the Cassini oval of each specific model type(non-electroporated vs. electroporated) allows for determination of the‘a’ and ‘b’ variable parameter and still satisfy the mathematicalcondition outlined above in the first paragraph of this section by wayof least square fits such as the NonlinearModelFit function inMathematica or via interpolation tables as the one presented below.

The interpolation method involves assuming values for the ‘a’ parameterfrom 0.00 cm to 3.00 cm in steps of 0.01 cm and calculating the ‘b’parameter using the specific points from the previous paragraph. Thedistance and steps were arbitrarily chosen and can vary depending on thespecific Cassini oval that is being developed. In the case of Table 9the point p1x=(1.70 cm, 0 cm) and the point p2y=(0 cm, 0.49 cm) and thecorresponding distances to either q1 (−a,0) or q2 (a,0) are calculated.

TABLE 9 ‘a’ d(q1, p1x) = d1 d(q2, p1x) = d2 d1*d2 d(q1, p2y) = d3 d(q2,p2y) = d4 d3*d4 d1*d2/d3*d4 1.04 0.66 2.74 1.808 1.150 1.150 1.322 1.371.05 0.65 2.75 1.788 1.159 1.159 1.343 1.33 1.06 0.64 2.76 1.766 1.1681.168 1.364 1.30 1.07 0.63 2.77 1.745 1.177 1.177 1.385 1.26 1.08 0.622.78 1.724 1.186 1.186 1.407 1.23 1.09 0.61 2.79 1.702 1.195 1.195 1.4281.19 1.1 0.60 2.80 1.680 1.204 1.204 1.450 1.16 1.11 0.59 2.81 1.6581.213 1.213 1.472 1.13 1.12 0.58 2.82 1.636 1.222 1.222 1.495 1.09 1.130.57 2.83 1.613 1.232 1.232 1.517 1.06 1.14 0.56 2.84 1.590 1.241 1.2411.540 1.03 1.15 0.55 2.85 1.568 1.250 1.250 1.563 1.00 1.16 0.54 2.861.544 1.259 1.259 1.586 0.97 1.17 0.53 2.87 1.521 1.268 1.268 1.609 0.951.18 0.52 2.88 1.498 1.278 1.278 1.633 0.92 1.19 0.51 2.89 1.474 1.2871.287 1.656 0.89 1.2 0.50 2.90 1.450 1.296 1.296 1.680 0.86 1.21 0.492.91 1.426 1.305 1.305 1.704 0.84 1.22 0.48 2.92 1.402 1.315 1.315 1.7290.81 1.23 0.47 2.93 1.377 1.324 1.324 1.753 0.79 1.24 0.46 2.94 1.3521.333 1.333 1.778 0.76

In the baseline case analyzed above when the variable parameter ‘a’ was1.15 cm the calculated b² were 1.568 and 1.563 for the d1*d2 and d3*d4,respectively. The last column calculates the ratio of both b² values inorder to determine the location at which they are the same (or closest)which happens when (d1*d2)/(d3*d4)=1.00.

Once it is determined that ‘a’=1.15 cm provides the closest ratio toone, the average of the d1*d2 (1.568) and d3*d4 (1.563) quantities iscalculated and used to determine the corresponding ‘b’ parameter bytaking the square root as shown in the equation below.

$\begin{matrix}{b = {\sqrt{\frac{\left( {d\; 1*d\; 2} \right) + \left( {d\; 3*d\; 4} \right)}{2}} = {\sqrt{\frac{1.568 + 1.563}{2}} = {\sqrt{1.5655} = 1.2512}}}} & (5)\end{matrix}$

Once the ‘a’ and ‘b’ parameters are determined then any plottingsoftware can be used to illustrate the Cassini curve in Cartesiancoordinates using the modified equation

$\begin{matrix}{y = {\pm \sqrt{{- a^{2}} - {x^{2} \pm \sqrt{b^{4} + {4\; a^{2}x^{2}}}}}}} & (6)\end{matrix}$

The steps outlined in the previous paragraphs just above can also beused to determine the ‘a’ and ‘b’ parameters using the same methodologyand with points p3x=(1.99 cm, 0 cm) and p4y=(0 cm, 1.01 cm) and resultsin ‘a’=1.21 cm and ‘b’=1.578 cm as the Cassini parameters for theelectroporated model when σ_(max)/σ₀=3.6.

TABLE 10 ‘a’ d(q1, p3x) = d5 d(q2, p3x) = d6 d5*d6 d(q1, p4y) = d7 d(q2,p4y) = d8 d7*d8 d5*d6/d7*d8 1.1 0.89 3.09 2.750 1.493 1.493 2.230 1.231.11 0.88 3.10 2.728 1.501 1.501 2.252 1.21 1.12 0.87 3.11 2.706 1.5081.508 2.275 1.19 1.13 0.86 3.12 2.683 1.516 1.516 2.297 1.17 1.14 0.853.13 2.661 1.523 1.523 2.320 1.15 1.15 0.84 3.14 2.638 1.531 1.531 2.3431.13 1.16 0.83 3.15 2.615 1.538 1.538 2.366 1.11 1.17 0.82 3.16 2.5911.546 1.546 2.389 1.08 1.18 0.81 3.17 2.568 1.553 1.553 2.413 1.06 1.190.80 3.18 2.544 1.561 1.561 2.436 1.04 1.2 0.79 3.19 2.520 1.568 1.5682.460 1.02 1.21 0.78 3.20 2.496 1.576 1.576 2.484 1.00 1.22 0.77 3.212.472 1.584 1.584 2.509 0.99 1.23 0.76 3.22 2.447 1.592 1.592 2.533 0.971.24 0.75 3.23 2.423 1.599 1.599 2.558 0.95 1.25 0.74 3.24 2.398 1.6071.607 2.583 0.93 1.26 0.73 3.25 2.373 1.615 1.615 2.608 0.91 1.27 0.723.26 2.347 1.623 1.623 2.633 0.89 1.28 0.71 3.27 2.322 1.630 1.630 2.6590.87 1.29 0.70 3.28 2.296 1.638 1.638 2.684 0.86 1.3 0.69 3.29 2.2701.646 1.646 2.710 0.84

In FIG. 23 , it can be seen that with the implementation of thepre-pulse concept to determine the ratio of maximum conductivity tobaseline conductivity one can derive a Cassini curve representing zonesof ablation. In this case the 500 V/cm isocontour was specified but thistechnique could be used for any other isocontour that perhaps couldrepresent the lethal IRE threshold for any other tissue/tumor type.

The polar equation for the Cassini curve could also be used becausesince it provides an alternate method for computation. The currentCartesian coordinate algorithm can work equally as well by using thepolar equation of the Cassini curve. By solving for r² from eq. (4)above, the following polar equation was developed:r ² =a ² cos(2*theta)+/−sqrt(b ⁴ −a ⁴ sin²(2*theta))  (5)

and the ‘a’ and ‘b’ parameters should be determined as previouslydescribed in this application.

The present invention has been described with reference to particularembodiments having various features. In light of the disclosureprovided, it will be apparent to those skilled in the art that variousmodifications and variations can be made in the practice of the presentinvention without departing from the scope or spirit of the invention.One skilled in the art will recognize that the disclosed features may beused singularly, in any combination, or omitted based on therequirements and specifications of a given application or design. Otherembodiments of the invention will be apparent to those skilled in theart from consideration of the specification and practice of theinvention.

It is noted in particular that where a range of values is provided inthis specification, each value between the upper and lower limits ofthat range is also specifically disclosed. The upper and lower limits ofthese smaller ranges may independently be included or excluded in therange as well. The singular forms “a,” “an,” and “the” include pluralreferents unless the context clearly dictates otherwise. It is intendedthat the specification and examples be considered as exemplary in natureand that variations that do not depart from the essence of the inventionfall within the scope of the invention. Further, all of the referencescited in this disclosure are each individually incorporated by referenceherein in their entireties and as such are intended to provide anefficient way of supplementing the enabling disclosure of this inventionas well as provide background detailing the level of ordinary skill inthe art.

The invention claimed is:
 1. A system comprising: at least one electrodeconfigured to deliver at least one electrical pulse to a target tissue;a generator in operable communication with the at least one electrodeand configured to send the at least one electrical pulse to the at leastone electrode; and a treatment planning module configured to be inoperable communication with the generator; wherein the treatmentplanning module comprises instructions stored in a memory that, whenexecuted by a processor, cause the processor to measure a response fromat least one AC voltage pulse to optimize treatment planning for anelectrical energy based treatment comprising at least one DC voltagepulse.
 2. The system of claim 1, wherein the treatment planning moduleis configured to calculate the specific conductivity of the targettissue based on the measured AC voltage pulse response.
 3. The system ofclaim 1, wherein the at least one AC voltage pulse is configured to be atest pulse and the at least one DC voltage pulse is capable of inducingnon-thermal irreversible electroporation of the target tissue.
 4. Thesystem of claim 1, wherein at least one of the DC voltage pulses isbetween 1 Hz and 100 MHz.
 5. The system of claim 1, wherein at least oneof the AC voltage pulses is in the range of 1 mV to 10 mV.
 6. The systemof claim 1, wherein at least one of the AC voltage pulses is betweenabout 50 V and 500 V.
 7. The system of claim 1, wherein the treatmentplanning module is configured to estimate a target ablation zone.
 8. Thesystem of claim 7, wherein the target ablation zone is estimated usingone or more parameters chosen from voltage to distance ratio, edge toedge distance between electrodes, and/or exposure length of theelectrode.
 9. The system of claim 8, wherein the target ablation zone isestimated by curve fitting as a function of the one or more parameters.10. The system of claim 1, wherein the treatment planning module isconfigured to derive a baseline conductivity and a maximum conductivityof the treatment area.
 11. The system of claim 10, wherein the baselineconductivity and the maximum conductivity are derived using one or moreparameters chosen from voltage to distance ratio, edge to edge distancebetween electrodes, and/or exposure length of the electrode.
 12. Thesystem of claim 10, wherein the treatment planning module is configuredto generate an estimated 3-dimensional treatment volume based on theratio of the maximum conductivity of the treatment area to the baselineconductivity of the treatment area.
 13. The system of claim 12, furthercomprising a display device.
 14. The system of claim 13, wherein thedisplay device is configured to display the 3-dimensional treatmentvolume.
 15. The system of claim 1, further comprising a display.
 16. Thesystem of claim 15, wherein the system is configured to: measure abaseline and maximum conductivity of the treatment area; generate a3-dimensional treatment volume based on the measured baseline andmaximum conductivity; and display the 3-dimensional treatment volume onthe display.